IMHO, not sure why people are advocating against switching tanks in the pattern, that'd be my favorite place to switch. if anything happens, there's a runway right there, as opposed to having something happen a few more miles out at relatively low altitude.
When I learned to fly 48 years, ago, the standard was a power-off approach. Downwind was level until an appropriate point, then the throttle was closed and the approach carried out power-off throughout the base and final, adjusting flaps (or slipping, or adjusting pitch to steepen or flatten the glide) as necessary to reach the runway. It taught precision glidepath and speed control. I think it came out of military primary teaching.
At some point, the power-on approach took over, perhaps as result of the idea that everyone was going to be flying airliners someday. The approach paths became longer and shallower. When I became an instructor I had to teach it that way, but we also would fake a power loss on downwind to teach the student the old ways. The problem with the power-on approach is what the OP pointed out: can I reach that runway? Quite possibly no.
Now, if you switched tanks late on downwind and it quits, are you going to be willing to turn sooner or leave the flaps alone or do whatever it takes to make that runway? Or are you going to dork with the selector and other stuff and forget to fly the airplane? Having a pilot-induced engine failure so close to the ground, at an airport that might be surrounded by buildings, is not smart. The tiny chances of the engine packing up for other reasons is bad enough, without adding another factor that increases those chances. There's also the small chance that the selector mechanism fails in an airplane that hasn't been well-maintained, too. I've found that stuff badly worn out sometimes. Cessna has a little driveshaft with two tiny U-joints between the selector lever and the valve itself, for instance. It gets sloppy as the U-joint rivets loosen and wear.
High wings rule. They can be run on both tanks (most of them), reducing the chances of fuel mismanagement or system failure at a bad time.
And altitude means more time to work out a solution of some sort.
Edit: there's a fairly recent AD on some fuel tank selector placards. It addresses the problem of the Left and Right positions being reversed on some replacement placards.
https://rgl.faa.gov/Regulatory_and_...959c17278625826600479197/$FILE/2018-07-03.pdf
The Piper SB it references:
https://s3.amazonaws.com/pipercrm/Solution/19000/SB_1309.pdf
Reversed L and R positions means that you'd be drawing fuel from the tank opposite to what was indicated on the selector. You could be switching from the fullest to the lowest tank, for instance, hence the AD that forced compliance with the AD.
