Jiujitsu is not made to cope with strikes, thats the bottom line.
Thats why MMA and jiujitsu are two different things. When you are alowed to hit, everything changes. You can't work from the bottom anymore... If you do, you just give your opponent an easy target.
Catching/deflecting punches, wrist/bicep control, head movement, and an active guard are all concepts used in BJJ to cope with strikes. And a skilled BJJ player can definitely finish a fight from the bottom despite strikes. A great example of a top-tier striker using BJJ to finish a fight from the bottom is Silva vs Lutter.
In the cage, anyway. Like I said it's not a great idea in the street but that has more to do with the lack of rules (eyegouging can really ruin your day) and the possibility of his homies ganging up on you while you're down.
Everybody good, plenty of slaves for my robot colony?