When I opened my bank account years ago, I had various different paperwork, lease agreement, visa, passport, work permit, etc. The person at the counter told me 'no'. I explained the website said I could, she called a few people, eventually she opened the account for me. Over the years on this fb board - I have seen several posts like yours. The conclusion - you may have to go to a few banks, be persistent (but not an asshole).
The TM.6 isn't so important - but I suspect that's not what your're talking about. I think you're talking about TM.47
If you plan to be in Thailand longer than your original paperwwork/visa - you will need to 'check in' with immigration. If you are staying at a hotel they'll do this for you. If you are staying at private residence (or airBnB) you will need to make sure this gets done. That means you will likely need to do it yourself. Brother's wife can do it for you and if she is nice, she will do it for you. She probably speaks Thai and you probably dont.
My landlord made a photo copy of his passport and house-book (brother's wife's national ID card, and her house-book). My landlord scribbled on the page - OK for [your name goes here] to do complete TM.47, then signed. So.. scribble [TM.47 - clear to read] scribble scribble scribble all on a photo copy of a passport.
I showed up at immigration with the above and photo copies of my TM.6, passport detail page, and visa page. I was out in 15 minutes. Or they'll ask for some more copies of stuff.
This page explains better. The key is you only need to do this if you will be visiting immigration for any other reason in the future. If you plan to leave Thailand in less than 30 days or before your visa expires - this step isn't required
I have used transferwise - as do many on this site. I have a local bank account as well as one in my home country.
You believe local bank account is required. They're easy to get but you may have to go to a couple of branches to find the right branch manager (who decides if they will give you an account).
Transferwise is reliable(ish) Sometimes money arrives in seconds, sometimes in days, usually seconds. But they will tell you at the time of transfer so it's not a mystery
Last week I flew from Phuket into BKK, then took a taxi to Pattaya. The next day I took a private car from Pattaya to Pattaya Airport, then back (retrieved my motorcycle). I was not stopped once.
Come from Penang to Thailand I was asked to show I had the cash. I have been asked to prove I had the cash when getting the visa. But never been asked at the airport