I’ve actually purchased higher-quality rectangular bags (better than the cheapies the grocery store has for sale). I also own some net bags.
The net bags are indeed easy to compact and shove in a pocket.
However, if you’re loading up on a big grocery run, they’re a PITA for the poor cashiers filling the bags (or for me, if I’m doing self-service checkout). The canvas (or recycled soda bottle or recycled cotton or whatever) bags are as noted a LOT easier for a big grocery run.
The one thing the string bags are great for is something like a farmers’ market. I can make purchases at one stall, put the straps over my shoulder (mine have loooong straps), and have my hands free for the next stall.
Shameless plug for the place I got mine: http://www.reusablebags.com/
The cheapie ones the grocery sells are of some sort of pressed fiber which seems to tear a bit too easily (and the seams come undone). I guess you get what you pay for. Our store used to have nice, very heavy-duty plastic-coated mesh bags for sale - haven’t seen them in years but we have some of those that are older than the kids.
Oh - and compactness isn’t a huge issue since I like most suburbanites go grocery shopping with a car, and the bags live in the car. I’ve actually even gotten to the point where I remember to bring them into the store with me (formerly a huge failing of mine). Reusablebags does have some very compact non-string bags; I can’t comment on how well they work with standing up while you’re filling them.