Aren’t the two main transducers, speakers and cartridge, the most important?

Nope. Two ends of the same chain. Ones important IMO of many. I'm torn and don''t think it is black & white. In the opinion of most of the yesteryear that I learned from, the cartridge is the least of importance in the vinyl chain. I believe speakers are at the top of the list but is dependent on the amp. The lower the db rating of speaker, the more power usually needed. This isn't set in stone but it is predominate in thought.

Your huge improvement from Townshend Podiums answers your own question: No. In fact we just had a recent discussion where all the really experienced vinyl guys agreed the turntable and arm are more important than the cartridge. Likewise if you notice the Podium you put your speaker on matters more than the speaker. For proof, $4k Moab on $2k Podiums total $6k sounds better than $9k Ulf. So the Podium matters more than the speaker.

We could go on all day, from one component to another, with examples. The best you can say is if your speakers or your cart are truly crappy relative to everything else then yes in that case they are your most important to fix. Generally speaking however, no. Not even.

Yes, I’d say so.

Mechanical transducers are well known to be the areas where the greatest amounts of measurable distortions are to be found.

You could say the same about microphones which are often said to be like loudspeakers in reverse.

The entire world and their dog seem to have given up even trying to measure distortion in digital formats, cables and amplifiers (non tube) decades ago.

The transducers (speakers, phono carts) tend to have more impact on tonal balance and overall sonic presentation than most components, and is a reasonable place to focus early in the game or when you want big changes, but we still hear the sum total the system like a chain. Sort of like looking through multiple pains of glass at a picture of a band/orchestra (envision a few water spots on each), the system is only as good as the weakest link...one extra dirty, distorted, or tinted pain, and the whole system is affected. If your system has multiple colored/tinted/distorted pains, then you’re enjoying a kaleidoscope.