I have a similar background, though in an obscure style of Japanese karate. I can't really comment on ground fighting since anyone with Japanese jiu-jitsu will wipe the floor with me (probably litterally ;-) ), but I can say something about striking.

I will probably start an argument, but a great deal of strength is unnecessary if you are trying to damage your opponent with strikes. When I say "damage" I mean "cause injury". You want to deform your target so that it breaks. To do so, you need speed, not strength.

Consider, for a moment, a glacier. Because it is ridiculously massive, it has a huge amount of momentum as it creeps along at 5 cm per year. A glacier can level mountains, but anyone can stand next it it and let it "hit" them with no damage. That's because it is moving very slowly and your body has plenty of time to adjust itself to any deformation the glacier will cause.

Now consider a bullet. It has not even a fraction of the momentum of the glacier, but it can drill holes in you. That's because it is moving very quickly. When it hits you, your body deforms and there is not enough time for it to adjust before it has deformed to the breaking point.

Another good analogy is Jello. Put some Jello on a plate. If you are careful, you can push the Jello around. It deforms when you push on it, but then rebounds and moves backwards, bouncing back to its original shape. If you push too quickly, though, there will not be enough time for it to rebound and you will create a hole.

Striking in fighting works the same way. There is not enough space in a comment to explain how to use this idea to strike optimally, but most people with good technique can seriously damage any human opponent. Certainly any adult (whether male or female) that has trained for 10 years or so will be "strong enough".

Strength is important in grappling and positioning an opponent. It is also important when you are wearing pads designed to deaden the impact of a strike. If the pads deform instead of the body, then if you want to knock someone out (for instance) you need to be very strong to physically move their brain case around. Similarly, strength is important to push their muscles around to tire them.

Part of the problem is that in sport we are hoping to have a competition in which people compete but don't unduly injure each other. In such a situation, strength will certainly play a big role and so women are at a disadvantage. If we were intending to see how fast we can injure our opponent (very possibly killing them in the process), then I think it levels the playing field considerably.

Jiu-jitsu is designed to constrain striking attacks so as to make them less dangerous, so possibly it wouldn't make any difference anyway -- a very skilled striker may not get many opportunities before they are taken down. However, I think we will never really know because I don't think there is any way to be really effective in striking without intending to kill your opponent. IMHO it is not a technique that lends itself well to sports (it is worth noting that the head of my style disagrees on this point!) I have also never seen an MMA fighter that strikes well (fast enough, choosing the correct targets, relaxed enough, etc). I don't think I ever will because such a fighter would injure too many people to get fights.