Nope, that's just not how banks work. A bank is not generally going to just let you arb them like that for fun because, well, meh we'll make money from OTHER people but we feel like making an exception and incurring an obvious loss for fun with this millionaire by simultaneously lending them money at a low rate and then paying them a higher rate for them to deposit it back with us.
In fact, the reality is the opposite in general, at lower amounts you may well find some promotional rates - switch your current account and pay your bills with us and we'll pay X% with limits to it.
What you're saying is akin to your local shop selling you stuff at a lower price than they paid at the wholesaler - why would they want to do that in the general case? The wouldn't save for perhaps some promotions. It's kinda fundamental to being a shop that they sell things for more than they paid for them. Likewise, it's kinda fundamental to being a bank that they're lending for more than they're borrowing.
Well, since
TIME moves forward and rates move with it..and most of us lock in a mortgage rate for a fixed 2, 5 or 10 year period.
For the last decade, when the interest rate was on the floor, this wouldn't work, but currently, let's say I won the lottery now....and use my own house as an example, as I already locked in my rates at 3.5% until the end of the term, I can get savings interest rates much higher than 3.5%. It works fine.
Yes, i know what you are going to say, you are going to say that doesn't work if you had to take out a new mortgage today....but i am using myself as an example. So yes, I know it is dependent on the rates going up, but right now....the fact is that they are and expected to for the coming months at minimum.
Time is a variable here, you don't take 1 snap shot of the rates on 1 fixed date, but because you can fix your mortgage rates, and also able to move your savings around in the future. With the interest rates heading in an upwards trajectory, this can work, in my example, it does work. There are people who gives out higher interest, and there are people who offer a lower interest rate. You don't need to keep your savings at the same bank as your mortgage. Actually I have a 5% savings account at Barclays and my mortgage is with them at 3.5%....granted, the savings cap is lower than the mortgage balance. Keep the rest at another savings account at 3.7%, which is still higher than my mortgage rate.
And yes, I know what you are going to say, if it goes down, then you are stuffed....well, not really, then you just pay the mortgage like everyone else, or pay it all off in 1 lump sum.