toman, no; I agree! I like to hear the bass when I go see a show, but statistically speaking, most soundmen are guitarists, if they play an instrument (mostly as a function of the fact that a lot more people play guitar than any other pop instrument).
There are a few session guys that have *great*, versatile tone on something other than a P (Nathan East comes to mind). I personally do not like the tone of a P bass that much; however, it does sit in the mix very nicely without much tweaking. To quote TB's own Basshole (Marcelo Gilberto):
"The tone is very mid-rangey and somewhat like a wah pedal, slightly backed off. There are less highs, and less lows than with a more modern "hi-fi" tone. This "honk" is what makes it cut through mixes, and blend well with other instruments. Its tone doesn't get buried in the kick drum, and it doesn't compete with the guitar and keys. It just sits perfect in the mix. Solo'd, it may not sound as wonderful as a modern "hi-fi' boutique bass, but in context, it excels. Anyone who's ever spent a long time getting what they thought was a wonderful bass tone, only to find that it sounded like a dog fart, or got lost completely in a band context, knows what I'm talking about.
Most consumer audio reproduction systems are lacking in low end response. That boutique bass may sound wonderful on a good system...on the big studio monitors, but it may dissapear on the midfields, and nearfields...as well as most of the consumer gear out there. A P-bass has this magical ability to transcend even crappy TV speakers. It is perhaps the most important thing any bass can be - it's UNIVERSAL.
Just like anyone who has ever done any recording/engineering (I have) knows, the monitors you choose to mix on have everything to do with creating what I'll call a "universal mix" - something that translates well on different playback equipment without swallowing or highlighting different instruments on certain systems. This is why to this day, so many people still mix on those horrible Yamaha NS-10s - not because they sound good (they don't), but because the resultant mixes tend to be universal.
I used to mix on Tannoys, but I found that the mixes, though very good, were considerably-less-than-universal. On some systems, the kick would pop out, on others, the snare, and on yet others, the guitar...etc. It wasn't until I procured a set of Genelecs that my mixes seemed to take on a "universal" quality, and sounded pretty much the same, almost regardless of playback equipment (they were also more gentle to my ears, and far less fatiguing - can't say good enough things about the 1030a's).
THIS is what the P-bass excels at, IMHO. Specifically BECAUSE of its "limited" frequency response, it has just the right sound to blend easily in a mix, not get mashed up with any other instruments, and remain pretty much in the exact same "space" sonically speaking, regardless of whether you're hearing it on the big JBL 813s, or the "Horror Tones" (Auratones)...the massive modern car system with four 15" subs, or the wimpy TV speakers on your parent's old console set from the 70s.
I own a number of very modern basses, as well a some higher-priced boutique stuff, but the P-bass ASKS to be played. It returns pure joy, with no muss, no fuss.
Surely, that counts for something."
To answer the original poster's question, I bring my custom-made Line6 Variax five-string to sessions. It can do the P-bass thing, but if I need a Jazz, MTD, Stingray, Warwick, Modulus, Alembic, 8-string, 12-string, violin bass, Thunderbird, heck, even a synth, I've got those, too, at the turn of a knob.
Left: stock Line6 Variax 705
Right: HJC Customs-modded Line6 Variax 705. Mods include the addition of a passive Seymour Duncan SSB-II passive pickup (with its own passive volume, passive treble cut, and independent 1/4" output jack), wide/flat neck (no radius, banjo-size frets, 34" scale with 2.125" (54mm) nut width, chechen rosewood fingerboard, with extremely thin asymmetrical profile), and matching chechen-rosewood thumbrest - my go-to session bass.
Far right: Close-up of HJC Customs modded Variax