Strike is important, yes. It depends on what level you want to play at. I'd take a guy who swings really fast over a guy who strikes it solid every time. The fast swinger can be taught strike. I think speed is largely God-given or at least learned at a young age child level. IIRC, studies have shown that kids who played stick and ball sports as a kid, even if not golf, develop the fast twitch muscles and hand/eye coordination much better than those who did not. And besides, the guy who swings fast is doing so much already correctly in his swing, he's probably not far off from strike anyway. Maybe face to path issues perhaps. Look at some Dennis Pugh's tweets about the importance of distance. Even at the pro level game, pretty soon all the short hitters will be eliminated. I said it before he arrived on tour when I saw him at Chambers Bay, because of Tiger guys like Cameron Champ who are athletes and the kids who have parents fortunate enough to afford launch monitors, will take over the tour. You're going to have golf overcome by super athletes. You won't see size 38" waistlines on tour for much longer.
If we go with your "majority of golfer" the same applies- you need reasonable speed in order to play well. It's that simple. That or move up to a different tee box. I'm making a big assumption and it's not completely true, but again, with speed comes some level of skill at swinging a club and with that, you can kinda see strike in there as well.
Probably, but how many people have a swing speed above 100 mph? Younger low handicap golfers might well be in the 100-120 mph range, but in reality they make up a small proportion of golfers (Probably less than 10% of golfers?). The majority are probably in the 85-95 mph range. It’s a big ask to get them into the 100-110 mph range, whereas they could all probably learn to deliver the club better quite quickly?
I don’t think I’m really talking about improving strike to a comparable quality of a tour player. I’m suggesting that some general improvement in how people launch the ball will make a big difference. The LPGA reference I made is really to illustrate the distance potential of better striking and optimal launch conditions.