Fighting in a well-tailored suit is no problem. I feel badly for women, who have to wear absurd footwear and clothing in some situations.
Fighting is one very unlikely task among many (running, dodging, climbing a fence, jumping or breakfalling) that may arise in various "emergency" scenarios, but given we're talking among martial artists, it's a good "wholesale task" to look at. The reality is, even looked at in terms of in normal circumstances, our clothing is not logical. At formal occasions half the women have bare shoulders and shins, while we guys have three layers including one with wool and a lining--plus a noose. No way is the air temperature in the room going to be comfortable for both, let alone the weather. But we all still play along. So if frostbite or heat stroke isn't our first concern in the way we dress--why would assault? It's just one consideration we work in with all the others.
Reality-based folks trained in street clothes for years. You know what we found out? Even though we'd readily wreck or filthy our favourite suits, clubwear, etc. in the cause of self-preservation if necessary, we don't want to do it on a weekly basis (e.g. in training) when something else will do. And like someone pointed out, when you train with heavy footwear, you can really hurt your partner.
The first take-home lesson from that was that our real-life clothing should be reasonable to get around in. Footwear that is comfy and grips well is the most important. Range of motion is next. Another consideration is lack of things that snag, or break.
Part of your training should be done not necessarily in what you normally wear, but in clothing that has similar properties to what you normally wear.
Training for street while barefoot is absurd, because the way you use your feet becomes totally different, whether kicking, moving around, on the ground... sport shoes--or best, WRESTLING shoes--are the norm these days. No stubbed toes, or sprained toes from hooking in your partner's gi sleeves, etc.
Common sense will tell you what you need to do. I've worked contracts in prison. I never wore a necktie. If I worked there full-time, I'd probably cut all my necktie loops and sew velcro into them, but it's just not worth it for me to do that at this point.
On one occasion I was attacked while wearing a necktie, and sure enough, the guy choked me with it. So what? There are a dozen things I could have done if I wanted, but it was just one guy, he was puny, he wasn't cutting off my circulation or air, and the police were already coming, so I waited it out rather than snap his wrist or cut out with a tac folder.
etc.
etc.
