The solution to the housing crisis isn't detached homes. It's higher density housing, better rent control, disinsentizing house ownership as an investment.
While I agree that SFH aren't the solution, what @rab is suggesting could be part of the solution. NJB talked about Streetcar Suburbs, which often consist of these types of homes but are illegal to build pretty much everywhere in Canada. Wartime houses (what I've always called them, I've never heard "Strawberry box houses" before) usually don't meet minimum lot size, minimum lot coverage, minimum setback, minimum parking, etc. as required in "modern" zoning, plus the roads they're built on are often too narrow to meet current engineering standards.
If people insist on having a SFH, these types of homes should be possible but our zoning has over-regulated and made it illegal to build anything different.
No, I think such low density housing is actually the cause of the problem, at least around the big cities. Toronto already has some pretty terrible transit times at the average being something like 100 minutes each way due to the distance from one's home to their work place. Increasing density is the only option, though as a compromise, I think townhouses are extremely good.
Get rid of front yards and just make all the houses long, and you can fit as much as 3 units with the same or greater floor space as one of those houses on a single plot of land. Combine that with tons of mid-rise apartments and independent housing is accessible to even those stuck on minimum wage jobs.
No, I think such low density housing is actually the cause of the problem,
Wartime houses are not low density though, they're medium density. Many are higher density than modern townhouses due to their efficient use of space (small rooms, tiny yards, limited parking, narrow streets, etc). Now, can those efficiencies be applied to townhouses? Yes! For example, the old rowhouses in Philadelphia or terrace homes in London, and these are an even more efficient use of space than wartime houses.
And once again, I'm not agreeing with @rab that we need to build wartime housing en masse. However, as NJB points out, these kind of homes are very desirable and I think there is a place for some efficient SFHs in the solution to this problem.
Those aren't only two options. May I present the Missing Middle. While high-density doesn't make a lot of sense in small towns due to the high per-unit cost to build, medium-density like townhouses, duplexes/triplexes/quads, and lower-rise apartment are actually cheaper per-unit due to shared infrastructure.
This. I'm perfectly okay with opening up the greenbelt as long as you make the density high-enough, and by "high-enough" I mean like Paris or Madrid or Manhattan. Pick a spot along the Lakeshore GO line and just build a station and a 10km surface LRT surrounded by a streetwall of eight-storey midrises.
I wouldn't say I'm "perfectly okay" with it, but I do feel a plan like yours is the "least bad option". For some of our housing supply, it might just be easier to build high-density on greenfield land rather than upzoning and running into NIMBYs. Paige Saunders has a great video which pretty much agrees with your comment.
The only thing I might change is which GO lines to build along as the Lakeshore lines are already the busiest in the system.