High-end TT setup with phono stage built in

Yes, SME Synergy. Not only all in one, but also one of the best turntables in the world at any price. Maybe even the best, period:

https://sme.co.uk/audio/product/synergy/

Why not just use a preamp or an integrated amp with a built in phono stage? 

I'm with brf.  It seems that's what you want, as an alternative to the SME Synergy type of solution (where the phono stage is built in to the TT).  And as someone else wrote, you could buy one of the many tiny, inexpensive, yet good phono stages now available and park them very close to your TT. Such a box could even be hard-wired to the tonearm (to avoid an extra pair of ICs in the signal path). Where have we gone wrong in our understanding of your post?

The SME Synergy doesn’t really solve the OP’s goal as there’s still an extra box to deal with. Any of the true all-in-ones are entry level units. As already mentioned, the best compromise is getting one of the small form factor phono stages and mounting it in an inconspicuous location. 

*If* I were looking for a TT with built-in phono preamp the Rose Gold Shinola Runwell Turntable would be a consideration. That would be for purely aesthetic reasons and a hail mary for the VPI engineering and support.

The Naim Prefix phono stage was designed to fit inside the Linn LP12, so is not visible when in use.

The Musical Surroundings Phonomena was specifically dimensioned to fit under the Basis 2000 series turntables.

So the OP is on the pursuit of form over function. Maybe a trip to Walmart is the solution. Maybe accepting that an integrated amplifier or receiver with a built-in phono stage is the solution? 

Sadly, my integrated amp of choice has everything (dac, amp, preamp, streamer and room correction) but no phono preamp (this was an overlook on my part, I thought it had a phono built-in). I have gone a phase of separates everything (tube monoblocks, preamp, amp etc), perhaps want to spend the next few years, with the convenience of one-box that can be left on all the time and sound great instead of switching on every damn box and waiting for it to heat up and sound great.

I will listen to more music and fuss less about the gear (with a one-box solution) was my theory. And so far that is true. With one system that can be kept on all the time and play music whenever I have a few minutes, I am enjoying my music collection that much more.
(I still have my monoblocks and DAC in storage for when I get through this phase and crave the midrange magic of the 300Bs)

My main reason about having all in one is that the work is done for me, I don't want to spend the time matching phono, tonearm, cart etc. I just (at this point in my life) want to listen to music, good music, crossing a level of satisfaction threshold (sure, I could do better getting separate pieces, but that 5% improvement is not worth it for me now). SME synergy sounds awesome actually (although it does have two pieces, wonder what is its price).

It seems like VPI player, and Rega P1 plus are the only options otherwise.
Perhaps I might have to succumb and buy a phono and a TT, which is a bit of a buzzkill in this minimalist phase of my audiofool life. But c'est la vie.

Thank you for as usual everyone for being ever so friendly and ready to help a fellow audiophile.

VPI Player? Not quite up to budget but if a lifestyle product is your requirement and you can improve the cartridge maybe.

Build yourself a Lenco based deck, you can make space for a phonostage in the plinth you build yourself, you get to pick the arm and they run off mains voltage.

You’ll have to try hard to avoid a turntable with a ps at the level you’re thinking of anyway so what’s another box?