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Canada’s policy towards Ukrainians compared to other citizens has already been very generous and the bureaucrats at IRCC actually warned against it because it would be problematic longterm. They also have their own pathway to get PR even if processing may take years without a cap unlike many other groups. Feel free to complain to your MP but tough to argue that Ukrainians are not being given favourable treatment and that they should also be given expedited processing. Also tough to argue that PR quotas should be increased to process more Ukrainians when they already have temporary status in Canada with access to things like healthcare unlike many other people applying for H&C. Would also be very tough to justify increasing the quota for H&C applicants versus economic pathways for example. In your case applicants also not contributing the tax base so even more difficult to argue for expedited processing compared to other applicants. For example quota for H&C also involves family trying to sponsor Sundanese relatives many whom are likely either still in a war zone or in neighbouring countries in less than ideal situations. The family in Canada have to guarantee financial support to get them to Canada which was not the case for Ukrainians and there is a pretty low number of applicants who will be accepted versus no cap. Although you may feel the system is unfair the data shows that your family member has been very lucky so far and with a reliable path towards PR remains very lucky compared to many other groups. I assume many younger Ukranians are trying to find economic pathways to secure PR so that may have some influence on processing times for Ukranians in the queue but don’t see any appetite from the government or Canadians in general to favour H&C processing or increase yearly PR targets to process Ukrainian H&C applicants faster. Also not possible to pause other forms of H&C to only or primarily process Ukrainians. If anything the argument would be for the opposite of what you are suggesting. Effort should be to process applications with no guaranteed pathway to PR who are inside Canada faster. Not trying to be mean just trying to provide some reality and perspective. H&C in general is a mess and needed reform a long time ago. We keep adding people and programs (there will be pressure to add more) while the quota decreases as does Canada’s ability to absorb people in need and who will place more demands on existing infrastructure.
Public policy means that the government of Canada had declared eligibility and and in practical terms had invited people who meet that eligibility to submit an application and receive a PR. A lot of people made life changing decisions because of this policy, sometimes through great peril and hardship.
Government has a duty of care to process those applications and get those people what they've been promised in a timely manner. And by timely I mean having a service standard and not putting people, many of whom are older parents/grandparent in limbo without any feedback for years.
I understand the pain of the government expense cuttings etc. But if the government makes a serious decision that affects lives and declares a policy (and make no mistake, I am very grateful that they did), it should be adequately funded and assigned resources. Otherwise it's not a government, it's a joke.

OTOH, H&C category is for people who've been rejected during the regular immigration process and are asking for some special consideration. That's not a public policy and not initiated by the government, so it's categorically different from our cases.
 
Public policy means that the government of Canada had declared eligibility and and in practical terms had invited people who meet that eligibility to submit an application and receive a PR. A lot of people made life changing decisions because of this policy, sometimes through great peril and hardship.
Government has a duty of care to process those applications and get those people what they've been promised in a timely manner. And by timely I mean having a service standard and not putting people, many of whom are older parents/grandparent in limbo without any feedback for years.
I understand the pain of the government expense cuttings etc. But if the government makes a serious decision that affects lives and declares a policy (and make no mistake, I am very grateful that they did), it should be adequately funded and assigned resources. Otherwise it's not a government, it's a joke.

OTOH, H&C category is for people who've been rejected during the regular immigration process and are asking for some special consideration. That's not a public policy and not initiated by the government, so it's categorically different from our cases.

H&C is for exceptional cases that don’t fall under other categories. The policy never guaranteed a certain processing time. The Canadian governent made some very irresponsible immigration decisions and welcomed a huge volume of targeted groups via H&C policies and refugee programs. The volume of applicants from programs like CUAET, Afghan resettlement program (not H&C but placed pressure on same services), HK, Iran, Turkey & Syrian H&C programs, etc. were always going to translate to a huge issues which is why IRCC warned internally about how the high numbers were not a good idea, set dangerous precedents and would lead to even more temporary residents trying to secure PR. Your family member not only had a relatively easy pathway to get to Canada (like no proof of sponsor or funds), financial support/healthcare after it was initially not pet of CUAET, fees waived, etc. which is not the case for many programs, etc. but also a path to PR. Not even all CUAET recipients have this guaranteed pathway to PR. Canada’s priority was to ensure the safety of Ukrainians and support our allies not to ensure a fast pathway to PR. The hope initially was that people would all be able to return home which is why CUAET was not a pathway to PR initially. Would you have preferred a very limited number of Ukrainians have been admitted under CUAET which may have resulted in faster PR processing for your parent if they had been lucky enough to have secured a spot? For some perspective Sudan has a larger population than Ukraine and their neighbours are much less able to support refugees yet if you contrast what was/is being offered to Ukrainians versus the Sudanese it should give you some perspective. Look at Gaza and the limited pathways to even sponsor family with full financial support. There are many in Canada with parents who live in war zones, poor conditions, without their basic needs being met, etc. and no pathway to come to Canada and especially no pathway to PR. I have a lot of empathy for Ukrainians but knowing the immigration history of Canada they are one of the few populations that have received special treatment compared to others for a variety of complex domestic and geopolitical reasons. To expect more seems both unrealistic and unreasonable. Also seems pointless because there is no political or societal will to increase PR numbers especially for refugees, protected people and H&C applicants or favour one H&C group over the others. You can certainly contact your MP but wouldn’t not expect it to lead to change for the reasons I have already discussed.