1. If every MMA fighter trains something, it's relevant to MMA.
2. The rules do matter. BJJ works better with no gloves or time limits. But most of the apparent loss of effectiveness is about everyone learning it, not the rules.
3. To be a BJJ based fighter in MMA you have to have good TDs. Most pure BJJ guys don't, though the exceptions like Demian Maia prove that a BJJ centric style can still be very effective if you can reliably get guys to the mat.
4. Sport BJJ has developed in a different direction than MMA BJJ, but that doesn't mean MMA BJJ hasn't and isn't developing. It is. You're seeing more leg locking, more non-wrestling oriented TDs (from guys like Maia and Tony Ferguson, for instance), and a greater synthesis of BJJ and wrestling.
In some ways old school BJJ was actually very lazy, in the sense that because only the Gracies and their students knew it you didn't have to work very hard physically or strategically to make it work. It was enough to put someone in your guard because they had no idea how to deal with it, and if you got their back you didn't have to worry about them getting out because they knew no escapes of submission defense. Well, now people know how to deal with old school BJJ so it doesn't work as well, you can't be as strategically lazy. Now you have to figure out how to get to positions where you can submit a knowledgeable opponent while not getting hurt, you have to know how to use your guard not only to submit but mainly to not get hurt until you can get back to a neutral position (because with punches, sorry purists, guard is an inherently inferior position and only a knowledge gap is going to let you win off your back consistently), and when you do get to a dominant position you have to know how to keep it while also doing damage and simultaneously setting up submissions or otherwise your opponent is going to get out. You also can't count on some silly Karate guy just falling into your guard or going down from a crappy single or clinch trip, you have to know how to take down other skilled wrestlers. A lot of the assumptions that made BJJ work so well in UFC 1 are completely false now.
Opportunistic BJJ doesn't work well in modern MMA because most guys are not going to screw up very badly. What you need now is BJJ oriented towards dominating from the start ala BTT/Carlson school. MMA BJJ has evolved towards better TDs and positional control oriented around striking rather than immediately submitting. In other words, it looks more like wrestling. So I guess if you're really interested in having effective BJJ for MMA get better at TDs and start worrying more if you can punch someone without being punched than if you can submit them. The days of a guard dominant, heavily submission oriented style of BJJ in MMA are done. It just doesn't work that well with rough equality of knowledge.