I think you should do high/very high intensity in only one or two lifts per workout. Using 1 to 3 reps in all the exercises will just burn you out. And your nervous system will not thank you yet again.
I'd actually say that you should be doing high intensity on only one or two lifts per week, not per workout. If 2, it should be 1 lower, 1 upper.
For something like the squat every day, my understanding is that volume is well-controlled, and that other lifting through the week is scaled back on intensity.
But the question you are raising is confusing to many. 5x5, 3x8, 8x3, 4x6, 6x4, 12x2, 2x12 all give you 24 or 25 reps, but they obviously won't all affect you the same way. I'm pretty sure that you can move a lot more weight 12 sets of 2 than you could on 2 sets of 12! Yet, the work load is the same. If you load close to your max for 12 sets of 2, you will have a much harder time recovering that if you do 2 sets of near your 12-rep max.
So you have to decide what your goal is for a particular lift, as well as your over-all goals in lifting. I have come to believe that when training for strength, you can make better progress if you focus on one lift at a time, rather than trying to get all lifts up at once. So you might, for example, decide that squat is where you want to put most of your effort for the next 6 months or a year. You keep the other lifts in your template, but you don't bust you guts on them week after week.
Then on the priority exercise you can work with higher work loads because you won't add as much fatigue through the rest of the week. It's like you have a budget of fatigue to spend. You can spend it a little at a time on all the lifts, or you can spend a lot of it on a priority lift, and less on the rest. Think of "overtraining" (and people can't really agree what, if anything that is) going over your budget for too long. Diet, rest and many other factors determine you "income", and determine how much fatigue you can recover from
Most people feel that they have to pick a rep-set combination and stick with it week after week, but you don't. When people do that, the only thing they change from week to week is the amount of weight on the bar. If you're not limited by a predetermined rep-set scheme, you can progress in many ways; add a rep to a set, or add weight to a set, or add an additional set. Like someone said earlier in this thread, if you do prescribed sets and feel you still have some gas in the tank, why not do another set? Even if it's not as many reps as your other sets, it's progress.