Its pretty simple: I'm not assuming materialist or a particularly optimal strategy. I could go into detail but it doesn't really matter, it was a super vague estimate intentionally. The takeaway is:
-if you play the game long enough eventually new pops will cause your research times to approach, with exponential decay, a very large research time. Fortunately, research will become less and less useful per-cost in tandem with this.
-barring some shenanigans with debris techs, the primary determining factor of victory in war is fleet numbers with research only deciding fights that were already mostly even.
-research is rubber-banded by its nature. Cheaper techs typically have a similar game impact compared to larger techs and larger techs are typically at least a little redundant. This isn't EU; if you've got 30 military researches and your enemy only has 20, you're probably MOSTLY on par assuming similar luck/meta knowledge/player skill.
Uh... a 10 military tech advantage? I think you're overstating things there. Between 10 techs I can easily get:
20% larger naval capacity (2 techs, 10% each)
75% more damage (2 steps up any weapon tech tree)
better PD/triple the shield capacity (2 steps up the shield tree)
etc. While any one tech isn't a lot, I think it should be pretty obvious that 10 different techs is going to be a major advantage. Numbers are important, sure, but part of what dictates the numbers IS tech. There are a ton of early +naval capacity techs in the first place.
-upgraded labs are the worst way to increase research. A lab IV costs 7x the minerals and 3x the energy credits compared to a basic lab. If you have literally NO other options, then they are MAYBE worth it. But until then there are far better uses of resources. Not to mention that researching a lab tech costs research points in the same field its supposed to be providing them.
Wait, slow down. You've got a couple things mixed up here.
Lab IV can only be built where you have an Empire-Capital Complex (ie, your homeworld). So we're mostly not talking about lab IVs, but lab IIIs. The mineral costs are an issue, but one that we haven't addressed elsewhere. But we'll assume you have some kind of mineral budget for infrastructure, obviously. I addressed the Energy cost above (which, again, is 2.5x, not 3x, because we're not talking about Lab IVs). Also the Lab III/Lab IV techs (which are the same) are t3/cost 1 techs that only cost 2320 base. They're not expensive.
Anyway, sure, a new basic science lab (lab 0) seems vastly more mineral efficient than upgrading a lab I to a lab II. But eventually you run out of pops to employ. At that point you can hold your minerals until you have more pops, or you can spend them now to get more output out of existing pops. Mineral growth increases way faster than pops, so guess which strategy techs faster? Probably the one where you're increasing tech sooner rather than later.
You'll also eventually run out of unblocked tiles to build on. At that point you need to start adding the cost of clearing to the cost of the next basic lab. Upgrading labs tends to win here, too. A basic science lab is 60 minus discounts. The upgrade is 90 minus discounts. But typical blockers cost 100 minus discounts. It's thus generally cheaper to upgrade to Lab II than to clear the tile. Of course even when you do clear all the blockers eventually, you'll still run out of tiles, and be forced to build a colony ship for 350 minerals plus the ungodly Energy costs of new colonies. And once you're on the new planet, you're back to square 1 (literally), waiting for pops to grow, building the necessary new energy and food buildings, upgrading colony capitals, building a new spaceport, etc.
Sure, if you have an unemployed (or underemployed pop) to build a building under, a new basic lab is the best use. But you run out of those pretty quick.
In short, research matters but not so much that you need to be thinking about it that hard. The only real rule is to take advantage of all "natural" researches and build a lab for, say, every 2.5 pops. Much more important it is to be smart about WHICH researches you pick. Remember, colonizing planets makes your research worse but it makes your everything else better.
I think you're totally neglecting the role of tech bonuses, which are part of why upgrading to labs IIIs (and IVs on your capital) beats spamming basic labs everywhere. Bonuses will tend to be centralized, because of mechanics like Assist Research, leaders, etc. Even if you're not a Materialist, you can use an Intellectual governor and Assist Research to get up to 100% bonuses, easily. But only on a single planet or two. And it's not like you can make pops grow any faster as the game goes along. Your 20th new colony grows at pretty much the same rate as your 2nd new colony. You are always be able to build/upgrade faster than pops reproduce. The new basic labs will produce 1 science with low or no bonuses (you don't start at 100 happiness/100 habitability) while your homeworld will always have all the necessary bonuses available immediately.
The difference is basically going to be "build new basic labs on a young planet and get (1*1.2) per category as pops grow" or "upgrade labs on home planet for additional (2*2) per category right now."