this post talks about the high octave sounds and continous frequency. Both of these things worry me about buying strictly a bass amp.
That is actually a slight exaggeration. I have been playing bass guitar and moog bass for over twenty years, I know these things well.
Bass guitars do have dynamic peaks and decay transients, but the fundamental remains strong and has the longest decay of all the harmonics in a wound string. And the fundamental of a bass guitar puts the most demand on a bass amp and speakers. Continuous playing of a bass guitar is not much different of a power demand than the steady state tone of a Minimoog.
Headroom is the spec of interest. The dynamic peaks of bass guitars and synths puts a demand on the amp AND the speakers. If your bass amp doesn’t have sufficient headroom, then the amp will clip on those transients and your speakers may not be so forgiving of clipping.
My gigging amp of choice is an old 1979 Moog Synamp, built like a tank and has two 200 watt power amps - more than adequate for gigging. For studio stereo, you want minimum 100 watts at 8 ohms per side with a good subwoofer. I started out with a Crown D75 rated at 40 watts at 8 ohms per side and I quickly found it wasn’t enough.
Your real concern should be the speakers. Continuous playing of Moog bass timbres is the acid test of bass speakers, because there is a lot of excursion on the cone and there will be heat on the coil that has to be dissipated.
The larger the cone, the more efficient it is at moving air at low frequency therefore an 15" speakers has less work to do than a 10" speaker. The smaller the speaker, the further the in-out excursion it has to exercise in order to push the same SPL air pressure as a bigger speaker, and you risk tearing the cone. Cabinet construction and multiple speaker arrangements do impact the performance, witness the 4x10 Hartke cabinets popular with bassists (although I prefer 2x15).
The better speakers have more rugged materials in the cone. If the cone is stiff enough and does not flex/twist with large excursions then it is more efficient at pushing air pressure. The better speakers also superior material on the outer rim that can withstand extreme excursions without ripping itself to pieces. Nasty spikes from a Minimoog can reduce an inferior speaker to shreds.
Bass playing increases the current through a speaker coil and this generates heat. A speaker with a one inch diameter coil will not be able to dissipate heat as well as a two inch coil. There is less surface area on a one inch coil, so heat will accumulate faster and you will burn open a coil wire, resulting in a dead speaker.
That is why one poster in that thread blew his stereo speakers playing his synth through his stereo. You can easily generate nasty audio peaks with a synth. When you buy a record/CD, the mastering process at the studio tames those nasty peaks to minimize damage of consumer stereos, and it keeps the radio broadcasters happy. Stereo consumer hifi speakers are not designed to withstand the extreme transients that a synth can create, the speakers do not have large coils and the cones are not very rugged.