Interesting comment. How close are the strings on the basses you currently own? After reading your post I measured my own basses, set up to my preferences, using the top of the body (to eliminate any differences in pickguard height) to the underside of the low E string right at the end of the neck:
March 1973 Rickenbacker 4001 - 15/32"
September 2013 Rickenbacker 4004L - 9/16"
October 2015 Rickenbacker 4004L SPC - 1/2"
2010 Martin Keith Elfin 5 fretless - 13/32"
2011 Martin Keith Elfin 5 - 7/16"
I have owned a whole slew of basses by different makers over the past 4 1/2 decades (Alembic, Fender, G&L, Kramer, Martin Keith, Rickenbacker,
ZON - and others, as noted below, plus some I may have forgotten about!) that all have/had a relatively similar feel, as far as string height off the body goes. The only ones I recall that had somewhat
higher string heights were the Gibson, Höfner, Rick Turner, and Yamaha basses I have owned. I have never owned or played a bass the strings were in "incredibly close proximity of the strings to the body", so it would be cool for all of us to list these measurements on the basses we currently own.
Another bit of minutia for the TB statisticians.