Does anyone do that on a tourer palerider?
I can think of a fair few arguments against, including:
those dinner plate rear cassettes are expensive (barmily so to me)
I can understand performance MTBers using them where they want super simple fast changes on a demanding technical terrain, but this doesn't seem to me to be a great priority on a tourer.
It is always possible on a tour for a ring to develop an issue, either because you have pushed the wear too far or because of damage, and you are then faced with a bike with a slipping drivetrain - annoying and possibly dangerous. I have a bike (non tourer) with a single front ring (21 gear dual-drive) and that is currently slipping when I pull away from lights as of course all the wear at the front is on a single ring. With three rings you can work around things for a while until you can get a fix.
I would imagine that the vast majority of those bikes with dinner plate set-ups are day bikes.
Personally, gear wise for a tourer, I'd go for 9 speed, 22/32/42 or 44 on the front and the wonderful (and cheap) Shimano 12-36 on the back. Will cope with almost anything. Necessary bits fairly freely available.
Seems to me a wide range MTB cassette makes 'one by' a viable option.
I'm no gearing expert, but 40 at the front and 51 at the back sounds like it would give a low enough crawler gear.
I'm certainly no racer, so 40 at the front and 11 at the back would give a high enough top speed for touring.
No front derailer and associated cable and shifter would be a simplicity and reliability benefit.
I concede I'm no fan of front derailers, having had a couple neither of which could be persuaded to work seamlessly.
Outside of the OP's budget, I would be tempted by a hub gear.
The Rohloff I have gives all the range you need and is famously reliable.
Slight downside is it does have more drag than a derailer.
The Shimano Alfine 11 is a more realistic possibility.
It has a decent range, and I'm told the reliability problems that affected mine have been sorted.
Still £300 or more when laced into a quality wheel.