It can extract more flavor. The most fruity and sweet brews I've ever had were good espresso shots. The same beans in a pour over are still fantastic, but it's all amplified and more pronounced when made as an espresso shot. There's also a syrupy texture that you really can't get with any other brewing method.

All that said, every day I drink pour overs and aeropress brews--I don't want to drop the $1k+ on a proper home espresso setup.

That is completely up to your personal taste. I personally like both. Sometimes it's nice having an espresso in the sun. Other times I prefer taking fifteen minutes for a nice hot pourover

I think so. My daily driver for coffee is a Chemex since I can make enough for two in about 5 mins. I use reasonably fresh roasted beans I grind right before making the coffee. But whenever I get a good espresso based drink I recognize the step up in quality.

It's a different beverage. That may sound precious or twee to you but the flavors of the same beans prepared in these three ways will be different; there's no other way to describe it.

Espresso is going to be more intense, probably sweeter, and stronger.

Pourover is typically brighter and less intense, but obviously you drink more of it. When I make filter coffee, I prefer pourover.

I do not care for Aeropress coffee or its sibling French press; for me, the mouth feel and flavor are inferior to other brewing methods, but obviously this is a preference thing.

It is not comparable. The beverage is quite different. So many people have had badly made espressos in the past they may think they don't like or care for it. Properly made espresso brings out flavors and smells which are not extractable with the Aeropress. The extreme case is the extraction of fruity flavors from a specific class of light roasts. You can not do it with Aeropress. I have a manually operated press as my espresso maker (Espresso Forge) and I only use Aeropress while traveling.

Different. It's just a different way to enjoy coffee that is dramatically more creamy and dominated by different flavors extracted.

No, not better. It's just a different drink. Some like it more, some don't. Some (like myself) like both.

It's a much richer coffee; feels more substantial in your mouth.

Yes