Bit of both.
Initially train a single strike so you get good at it and can use it in several different scenarios. Or when you come across a new technique you want to incorporate.
But eventually you MUST be able to follow up and keep on going with other strikes, locks, whatever.. because as you found out, one isn't necessarily enough.
If you just train for one strike and it doesn't work and you haven't learnt to follow up, I predict that you will freeze when it doesn't work out for you.
You can use the same types of techniques in different ways.
For example take a palm.. and in this example you are pre-empting..
jab/cross palm (to chin or chest)
hook palm (to chin either side)
After that you may end up in clinch range, if they haven't gone down, you have elbows/headbutts/knees/locks/clinch techniques..
Same if your drills locks or restraints or whatever, you have to be able to go into other things if one doesn't work, because it doesn't always work. Sure i've had times where techniques have worked straight away, but many times i've had to try several different things before i've been able to lock a guy up.
It's a bit hard to communicate this stuff by text, but I hope it helps.
-Ben