I tend to agree but then I wonder why? As pointed out up-thread, nobody bats an eyelid at a pram, buggy or shopping trolley which arguably take up the same footprint and are often piloted with little care. What harm is actually being done by a bicycle in a shop, other than being a bit unusual? Perhaps with pro-cycling measures underway there will come a time that there will be too many bicycles at a shop to allow it, but then presumably the measures that put more people on bikes will include appropriate security at your destination that make the perceived need to keep your bike with you redundant.
Prams and wheelchairs aren't unstable. They do not fall over. They do not have dangerous cogs, sprockets, frayed cable ends, etc, that can cause injury.
Add to that most cyclists do not know how to safely and correctly push a bicycle, simply because they've never been trained to do so and have never bothered to research it for themselves - it is not possible to safely push a cycle
and have a hand free to lift items from the shelf, put them in a basket, etc. Indeed, the safe method of pushing a bicycle involves having the geartrain facing away from the rider for safety reasons - that exposes the geartrain insteadmto other shoppers in close proximity, which is nasty is something adverse happens.
The only viable alternative presented so far in this thread is a folded Brompton - other folding bicycles are available - either on a leash being pulled, carried in it's own bag, or in a trolley. Bikes are for roads, cyclepaths, bike sheds...not for shops.