G'day Simon and wazkelly...
It certainly is an interesting subject and I've found myself doing quite a bit of research on it over the past few days. I can certainly understand needing more watts to drive a speaker to generate more db's in the lower notes of the low B string, especially if driving a 15" speaker at gig volumes... Those wavelengths are getting pretty long and need a decent amount of movement to generate it at stage volumes to match the higher frequencies.
I can also understand your thought process wazkelly regarding the need for the extra wattage if you're not necessarily after the volume that a higher wattage system can produce. That raises the thought if you're increasing the watts (and in turn volume) to boost the lower frequencies then when you go to play notes higher up it's going to blast extra loud - so I'm not sure if just having more watts is the complete answer... I think what is really needed is an amp and speaker/cab design combination that has a flatter response in the lower frequencies that can cover a 5 string bass, regardless of what watts and volume you're trying to play at.
Manufacturers used to disclose the frequency response curves of their amps/speakers but I've noticed you don't see it much these days. I've been looking around to buy a suitable bass amp I can use at home to practice and can't find any detailed info on the current crop of smaller bass combos - they just advertise a Xhz - Xhz range in the specs and that's it. Usually the db drops off as it heads towards each end of it's range. I think that's what I discovered this on Monday night with the churches amp. I didn't seem to have much volume with the lower B strings yet the higher strings were quite loud. I ended up lowering the pups significantly on the treble side to try and balance it out. Last night I plugged the bass into a mixer then plugged my full range monitor headphones into it and the low B string sounded huge and full and the volume on the A/D/G strings wasn't as loud in comparison. The headphones were able to reproduce the full range of frequencies the B strings was offering up including all the subtle harmonics and overtones. I think when using an amp that can't handle the full fundamental notes of on the B string it ends up reproducing those harmonics and overtones more which could lead to the weak farty/sound.
So this leads me to think that if my headphones can pump out a solid sounding bass at hearing loss volume then a smaller decent speaker in a well designed cabinet should be able to reproduce a solid 31hz low B in all it's glory, even if it's just at practice/personal monitor volume if the amp and speaker/cabinet is designed and tuned to deal with those low end frequencies at sufficient db. It probably wouldn't handle stage volumes but that's when bigger and/or multiple speakers come into it along with all those extra watts to drive them.
I'm no speaker technician or audio engineer but that's how interpret it all based on what I've learnt over the years along with recent research.
I should also add the amp at church I was using is an ancient Ashton head with 1x15 cab which has probably seen better days. I have no idea of it's wattage but it wouldn't at all surprise me if the speaker is shot. The head is starting to have a few issues like random spikes in volume... quite frustrating as you have to continually monitor it and adjust playing intensity when it does it.
I ended up ordering a Trace Elliot Elf head and matching 1x10" cab today after reading and watching many reviews. I was initially going to just get small combo - eyed off the Fender Rumble 40, Hartke HD series or one of those tilting ampegs... Even toyed the idea off a larger combo like a 12" TC Electronics but figured it would be overkill for quiet practices at home as I don't really need the volume which would just peeve my family and neighbours off! The TE Elf is rated at 200W 4ohm/130W 8 ohm so that will probably be overkill still for home use but I figured it would be much more versatile being such a small head as I can pop it in the gig bag and use it at church and plug it into the 15" cab there and run DI out to the desk. I should be able to dial in some more consistent tones that way too.