I've been playing Stax, Motown and Muscle Shoals since the the late 60's. Having been alive when Leo designed his basses, during the early years of Leo's creation most recording bassists used a DB. The use of a PB in the studio in mass was a number of years after the fact. Most of the bassists ( like Jamerson) were DB players used to the dead thump of a DB hence the preference of dead muted PB.
Compression is not a recent development when is comes to recording studios, or radio stations for that matter. Records were mastered for play on AM radio until FM radio took hold almost 14 years after Leo's modern PB was developed. I'm sure there was other gear used and other recording techniques used that have gone the way of the dodo. I think one can get pretty close to that sound today, but AB it and I'm not so sure it's a dead ringer.
Frankly, like I said I've been employed to play this genre for over 50 year now and have been using new or relatively newer round wounds for 47 of them. Countless gigs rehearsals, and recording sessions. In this time I have never had anybody, band mates, band leaders, producers, or sound engineers suggest or insist I use flat wound strings.
I had one keyboard player once asked me why I didn't use flats. I turned on my amp, plugged in, and played one note. He responded " Oh I get it." Other comments I've receive come from sound men and sound engineers thanking me for not bringing in a PB with dead strings they can't do anything with.