That is why so many people question the law as it stands
It's fine to argue that the cutoff seems a little arbitrary, but the fact is that a bike which is completely legal for you to own and use without MOT, insurance and tax like a motorbike is completely accessible to you and furthermore the bike would be perfectly capable for the daily commute you've described. It would cost you very little per mile. Certainly cheaper than walking if you bought a couple of pairs of trainers a year. The whole thing would easily cost less than running even a very cheap car for a few months.
It feels to me that what you're looking for in this thread is confirmation that you can own a bike that isn't road legal but can still be used like a normal bike. And no-one knowledgeable about the situation would give you that reassurance because it's wrong. You might get away with it, but then all it takes is a crackdown. With the recent media attention illegal ebikes have had I wouldn't bet against a crackdown on their ownership. Not at all. If I was a police chief under pressure to show crimes being solved I could well imagine police stop checking commuter bikes and crushing them.
As someone with money I have third party insurance for my bikes (I took a calculated risk and decided that it wasn't worth insuring the bike for theft). They will pay out for my home converted MTB (I checked), but do you really think they (or any other insurer) would pay out if I killed someone riding a bike that broke the very clear legal definition of a pedelec? No, I'd get sued and maybe lose my house.
I spent many years working in the legal trade (specifically Wills) and I can tell you that a lot of Internet "experts" read stuff on the Internet then make very stupid decisions thinking they can get around the law. The fact is with all pedelecs the law is there in black and white and while I wouldn't call anyone here a fool I would argue deliberately breaking the law when you don't have to is not a wise decision.