Well I want to catch a longnose because I am trying to catch every species of fish in Ontario, and I haven't caught a longnose yet. (just the ones that can be caught on a rod and reel, I cannot see myself trying to catch any minnows, although there are people who fish for minnows). I do this because I love fish biology and really enjoy researching the different types of fish, their life histories and identifying them. It also provides a fun challenge to try and catch new things and explore new fishing locations.
This all started when I destroyed my shoulder and couldn't play sports anymore. So, I needed a new hobby, and I really liked fishing. My dad always told stories about a weird "dogfish" he caught as a kid, and I wanted to see what they look like. So I researched them, found a few spots around my house where they could be found, what people catch them on etc. Then I went to try and catch one and it was a blast! So, I expanded that to other species like carp, catfish, bass. Now the longnose sucker is the fish I haven't caught at this time of year, and they are not anywhere around my house back home, so this is the best shot I have at catching one.
As for why would you want to catch suckers in general, they are abundant, easy to catch, put up a decent fight, and taste pretty good (bones are a little annoying). I don't tend to keep many of them. I only end up keeping the smaller ones because I deep fry them to remove the bones, but the bones in larger ones don't crisp up as well. Apparently you can also pickle or can suckers, but I don't have the fancy equipment to try stuff like that.
Anyway, hope this is a good response, feel free to think I'm crazy. This is something I find fun, and I will keep doing it so long as it stays fun.