Pros - strength, reliability and possibly better tone. Push-connectors can work loose over time and/or corrode internally, making a bad contact or coming off entirely. Many are fairly cheap and flimsy, which doesn't help. The problem isn't just between the clip and the speaker tag, there's another contact between the wire and the clip, which is just crimped.
Cons - makes it harder to swap speakers. That's all.
I always solder, on my own stuff - and often as a reliability upgrade on customer's amps too.
I will be soldering soon I believe. Ive been swapping speakers like a mad man in the last two years and been using connectors because of it. I seem to have settled on mostly Tonespotters and G12-65's and I think I done. Bob
Solder - cold solder joint due to too much tin (a blob), solder creeping up into wire under the insulation will make the point where insulation a potential beak point. There should be just so much solder that wire strands are still visible but tinned.
Crimp terminals: wrong terminal type (size, one time or multiple use) crimping method - use dedicated crimping tool, don't squeeze with pliers etc.
Wire: don't use tinned stranded wire for crimping, use stranded copper.
When properly crimped the copper strands are pressed together to form a homogeneous cross section and copper is also pressed into terminal material so this also forms a homogeneous contact area.
Such terminal when pushed onto a proper receptacle will press into receptacle material and form a complete homogeneous copper wire to receptacle connection.
Crimp terminals are often preferable to soldering, but here is a trap: even if you crimp the wires properly the receptacle on the speaker is the weak link, this one is often tinned and after a couple push on pull off cycles will no longer make good reliable contact.
To summarize: it's easier to solder correctly than to crimp without proper tools.
Have your tech fit a pair of EV type spring loaded terminal posts to each of your speaker collection, and swap away, plug and play to your heart's content https://www.simplyspeakers.com/ev-speaker-binding-post-33750-33751.html
I guess there would be significant increase in parts cost to fit them to all speakers, the vast majority of which will be 'fit and forget'. And the least desirable market trend would be for cheap, low spec spring terminals to become the norm.
Solder the wire to the push on connector, then slightly 'crimp' the connector [if needed] so its a very snug and tight fit on the terminal. Road worthy + easy speaker swaps and your not de-valuing a nice speaker.
Sometimes the connectors just don't fit and, as suggested, can work loose even with perfect fit. And if You like the speakers and wouldn't consider to sell them off any time soon... bring forth the solder!