More than PMQs, I just wish the CAF built a lot more SQs. Even in non-Reg F areas. Simply providing that, means one less participant in the local housing market. Cheap SQ would be a great incentive to join the reserves. Especially given how difficult it is for a lot of students and young people to get decent and cheap housing and given how many of our reservists are students and young people. We can't seem to have government think of housing beyond silos though.
While I like your idea, I see some pitfalls:
1. What is the criteria for being allowed to rent one? ie. So many days attendance a month? Valid Force test? Green on ARV? etc...? You can't just allow reservists to rent them as you'll get people joining to get a place and never showing up (or just showing up enough to not go NES), but bringing no added value to the force.
2. Who is the landlord? CFHS can't manage/repair/upgrade the homes they have now. Giving them even more homes (away from Bases as you suggest) will only increase the speed at which they turn into crap if no one is looking after them.
3. You mention cheap SQs. That's partly why we're in the mess we are with housing. The local market will cry foul, the politicians will pander to them to get votes, and the price will jump to "fair market value", which in places like BC and Ontario, will mean rent is still unaffordable.
4. Who polices these SQs? Junior soldiers being how they are, I suspect there will be times when policing is required. If they are considered SQs, I imagine (happy to be educated on this point) that the MPs will have to/want to be the ones investigating the low end offences (trashing the place, quarrels, etc...)
5. Along with point 1 above, who is pri for getting these? There will likely never be enough to satisfy demand, so is it based on need (and how do you calculate that), Rank, time in (or lack of such), etc... And is it once your in, your in for life (or until you release at least)?
Anyhow you get my point. Until we can sort out/provide enough housing on major bases, I can't see this seeing the light of day. I wish I were wrong as it could help.