I apologize. I'm very late for the show here . In respect to Paul and his basses,action,melodic basslines and of course his using the Hofner when performing . On the White Album, he used a Fender Jazz,an early CBS Fender ( look at the machine heads ) . Michelle was the first song he used the Ric on, in the studio. I don't know if he used the Hofner again for recording ,with the exception of " Let It Be " .... Abbey Road sounds like a legitimate bass ,possibly the Rickenbacker. ( It definitely wasn't the Hofner on AR )
I've met Paul a few times and have talked with him quite a bit,but this goes back quite some time.
He is a people pleaser. One of the most real human beings I've ever met. You would never know he was one of the four. The Hofner, I'm sure serves two functions.first,it is so light and when you're doing close to three hour shows,at a " certain " age , I can understand that completely. Secondly, it's in Paul's DNA. If it wasn't for Paul, nobody would even know Hofner existed in the USA . It's iconic because of one man.
Personally, I like others feel it plays like a toy. Short. Scale ,not particularly well made ( look at the pups and machine heads ) and the sounds is not well defined,to me it sounds like a tuned bass drum. It would be virtually impossible to play slap bass on a Hofner.
Then again,with few exceptions, he used the Rick and Jazz from Rubber Soul, until Abbey Road ( LIB being the exception ) ...
Paul as others have suggested,wasn't a speed player, but he is without question one of the most melodic and tasteful players ever. Always seemed to play the best / correct / spot on etc. bass part for any given song. The fact that he wrote so many of them makes it all the other worldly .
Now to my point. As I'm sure you are all aware of Gibson EB1 violin bass. They sound like hell, in my opinion. Much like the Hofner.
So,in keeping with the idea of an electric bass,that has a small body,short scale neck ,lightweight and all that business .
Paul is an extremely wealthy man, has been for over fifty years. Why,oh why did he never sit down with an exceptional luthier,way back when, and say." I want a bass,similar in size to my Hofner, only I want one, that is handmade,from the best woods,hand carved hollow body with true F holes , ebony fingerboard between a short scale and full scale length , clover / cello machine heads ( you could design tuners in a 3/4 size fashion) two pups that have an ability, ( yet not realized ) that sound somewhere between an upright and electric bass and I'll work on it with you,regardless the cost. I want something light,well made, that has a sound like no other "
It could have been done. It may have to weigh a bit more,and body possibly a bit larger body,but still in keeping with the violin contours. Something like a horizontal cello ,only much,much smaller.
I'm seventy years old, been through the whole Beatles era, in real time ( There's a huge down side to that

...
I love the aesthetics of a string section,violin,viola,cello and contra bass . Just something about the visual of the instruments ,let alone the sound of an acoustic instrument.
People can say,that fifty some years ago,we didn't have the technology ,and even if we did, the laws of physics would dictate ,that what you are suggesting is impossible.
If we believe in that mindset,we are doomed to failure .
I play an old E series Fender p bass,57 maple neck,62 body, fretless.( had to have frets removed,as they didn't make a maple neck fretless ) High action ,flatwounds, and a 62 RI jazz fretted USA . I love Fender basses ,both serve a function. By the way the 85 E series 57/62 is EXACTLY QUALITY WISE SAME AS THE ORIGINAL US PRODUCTION MODELS ! Anybody that pays Fender for the crap they have been selling for past fifty years is being had. You have to pay $3000. and up for a CS, which is absurd. Get an E series 84-87 ,take out the pot/cap/1/4 inch and pups,replace with vintage harness and pups ,and you have the best bass money can buy. Hand wired ( soldered ) harness with oil/water cap,CTS or a number of other companies making caps, that are phenomenal,pups double handwound ( totally passive ) . You will even have a better bass than the originals. Cost for prewired harness with cloth pull back,pots,cap and 1/4 jack, best you can get will cost you $200. All hand wired . Double wound,if you like a lot of output $100. for the split p bass.
Same holds true for the jazz,only a bit more for harness and pups ,possibly $400. AT MOST !
P bass extremely heavy,but as I do sessions, I'm sitting all the time .
I've always maintained, if I had the fiscal resources, I would love to design a bass like,I'm describing about. Passive, not hot wired . I honestly believe it could be done. By short scale, I don't mean to the degree of a Hofner,something in the middle.
In closing. Has anyone ever heard of a bass like I described , in reality ? NOT the Gibson,they look great,but sound like hell, and again, an extended short scale neck. I understand the idea of balance . That said,these are all things that people with a passion for something figure out. Nobody to this day, thatnim aware of,produces an electric bass that sounds like an upright. ( I know, but that's amplification technology . Paul doubles some of his bass parts with an upright,this before Bill Blacks bass. Listen to break in " I'm Only Sleeping "
I'm new to this forum, so please bear with me, if what I wrote is redundant. If it has merit,please respond,would love to know what's going on in respect to anyone ever making a prototype violin Elec.Bass ...
Best
Jake