I can't speak to the United Nations interview queue with any professional knowledge.
Remember that the UNHCR is dealing with people who have just fled and have an immediate protection need, and they will often interview them within days and refer them to a country within days, which will resettle them immediately because the person is at immediate risk.
We also have populations who have been residing for generations in refugee camps. Canada was a very large participant in resettling Bhutanese from eastern Nepal. I was involved in it myself. This was a 20-year phenomenon so from a processing challenge point of view the UNHCR were there, set up a large operation, and it would take some time to set it up and they would interview people to meet the challenges.
It is of course true that the United Nations High Commissioner for Refugees, like all humanitarian agencies right now, is in desperate need of additional support and resources. Their appeals, given the catastrophic size of the humanitarian crises around the world, are not being fully funded. So yes, of course, they could use more resources.