Other than that, it would favor having more labs instead of just one and then only spamming nanos next to it.
That's the old TA gameplay. The reason people build only one lab is the nanos as you point out. From what I understood nanos came into play because people wanted everything to go fast.
As long as there are nanos I don't see why someone would prefer to have 2 labs instead of 1. There's not a real benefit if you are not overwhelmed with M and E. And if you are, then you would most probably build a t3 or a vulcan.
Making a 2nd lab is already beneficial, if they are next to each other it lets your nanos work full time instead of waiting for a unit to get out. Or building a 2nd lab nearer to the front (especially when compushing, you already have buildpower there to assist), so you don't have to wait for slow units to crawl into the front.
The incentive to build a 2nd lab is already there, as demonstrated by good players constantly doing it. This would just be a nudge to get more into that direction.
I think it should become extra harder to tech in general. Teching destroys the gameplay. I would like to see 200 t1 against 1 krog, not a spam of t3 :/
Teching is really hard as it is, if you don't play huge games.
Especially when for the last years the trend has been to just make t2 units stronger (bulldogs, panthers, crocs, etc.), obsoleting t1 units to a big degree when you get there. But getting to tech is still as hard as ever. But well, that's mostly unrelated...