I was just talking about this the other day. The only problem when you do reps of 1-2-3 is it is hard to add weight because it is so close to your 1RM. If I'm doing a work out of 5x5 at 70% ish it is easy to add 5ish pounds almost every week for along period. If I'm doing a work out at lets say five heavy singles or 3x5 at 95% or 85% of my 1RM it is going to be almost impossible to add any weight for more then a few weeks.
You do need a combination of both. Several weeks of 5's followed by a few weeks of 3's followed by a peaking phase. It is covered pretty well in :
https://www.amazon.com/Practical-Pro...s%2C230&sr=8-1
For more antipodal evidence I ran a 5/3/1 program similar to what you were talking about for most of last year and made minimal progress because the weight was to heavy to make much progress for most of the time. I ran one advanced program in Practical Programming for strength and made more gains in 11 weeks. *Disclaimer* Results may vary lol