About 15 years ago, I got tired of liners that were chafing, too tight, or too loose. Or, the liners would wear out before the shorts. I thought, "Why not just cut the offending liner out of the shorts and wear briefs made specifically for running?"
Back then, I was limited to Asics and a couple of other brands of running briefs. Today, many performance briefs and boxer briefs exist. In summer, I wear mostly Asics or an off-brand of wicking fabric briefs... looking up the brand now... Papi. In winter, I wear boxer briefs, especially Puma, RBX, and Spyder. I've tried several brands, but those are my favorites. You can get a 4-pack of performance boxer briefs at TJ Maxx for $12.99 so it's easy to try lots of options. When I find a brief I really like, I go back and buy 10-12 pair. It sounds like a lot, but yesterday I ran, changed clothes, worked out for nearly two hours, changed clothes, and then ran some errands. That's three changes of underwear.
Since the liners wear out before the shorts, this extends the life of the shorts and gives me the fit I want regardless of which pair of shorts I wear. It also gives me the flexibility to buy shorts without a built-in liner or to buy shorts that I really like but the liner doesn't fit.
When I buy a new pair of running shorts, the first thing I do is cut out the liner. Just be careful not to cut out the key pocket.