My feeling is that if you're after an elite international coach to push forward one of the top tier nations, then you don't pick Baxter.
Afterall, could you see Australia, new Zealand, South Africa, Wales even having him on a shortlist?
However, as an English coach, and given how he has consistently improved Exeter to becoming European and domestic champions, he deserves to at least be added to the discussion for next England head coach.
Afterall, his success should merit some form of reward.
The fact that he seems like a genuinely good guy probably doesn't carry much weight with the RFU, but it would with me.
I'm not sure who I'd choose to replace Jones, but if it was to be Baxter, I'd support him 100%