I love automatic TTs. I wish some of them sounded better. I'm starting to sound like a broken record, but some of the great Japanese TTs of the 1970s and 1980s had substantial automation - even among the greats. And Raul points out that it's easy to install an aftermarket armlift (and there are a lot of VTA-on-the-fly jigs out there too). The table I am using most of the time recently sounds great, has (manual) VTA on the fly, and auto-lift/auto-return. I have to cue the record myself but I have resigned myself to that... :^)
With all the re-plinthing of Garrard 301s/401s, Thorens 124s, and Lencos going on, I am surprised I have not seen someone build a phono pre and MC stage into a big plinth (and if one really tried, one could put an ADC in there too with a USB jack output). Talk about one-touch convenience...
If one wanted super-duper-easy, one could try a Denon DN-308F-T. The arm is not automated (but autolift could be added), but you can cue/drop when the record is stopped, and then one button for the on-switch, and one twist of the Attenuator-Start dial and you get the play button and the volume in one twist. Autolift can be added. It already has a mono/stereo switch, MC headamp, phono stage, and line amp built in. And there's plenty of place in the chassis for some chip amps (if one could build them with XLR inputs) and then all one would have to do is connect speaker cables out the back. Hmmm...