For my personal guitars and basses, there aren't many that I haven't done this to, @Owen. And where practicable, I have always favoured doing it for custom builds too. It usually isn't the actual depth that is the issue to the player (and there be dragons in the spine zone), but instead it is the 'haunches' either side of the neck spine that generally makes the biggest difference. That can make a MASSIVE difference to the feel of the bass or guitar. I have been able to show more than one player that the 'slimmest of the necks that they have ever played' is actually deeper than the rest of their collection.
So when I have ever built a bass or guitar for myself, I carve the neck close to what 'feels right' but then, when it is fully finished, strung up and in tune, I play it, then twist it round like a back to front cello and shave material off the haunches from the heel to the nut, either side of the central spine. Then I play it, then turn it round and shave some more off until it 'feels right'. Finally I re-do the slurry and buff and by the next day of it hardening off, I have a fully playable bass or guitar.
It's clearly a little more involved if it's a varnished neck, but you can do the same with those.
Tone-wise, I've never been aware of any major difference unless the spine itself is reduced - and never do that unless you know exactly how deep the trussrod slot is...