On its own, might isn't very good. As a secondary tree, it's VERY good when combined with Prosperity. For me, it easily rivals industry as a secondary tree. Try this --
Open and go down might to scavenging. Build a small military and slap the aliens around. Get at least marines (level 2 any affinity) ASAP.
Switch to prosperity and do the normal thing -- free settler, mind over matter, joy through variety etc. You'll probably get a free 2nd or 3rd colonist via the free colonist virtue, not your first. HOWEVER ...
Before getting any tier 2 affinity tech (not the inner-ring), snatch "Adaptive Sciences" in might. It's only four into might, connected to scavenging (you have that already!), and gives a +20% boost to any tech that gives you affinity. This will get you your last affinity level for victory (usually 12!!! in this strat [read below]) about 20-40 turns sooner, possibly more. It will also allow you to enable certain units WAY before you'd normally be able to get them. For example, getting tier 1 purity, completing two beginner quests in purity, and getting a tier 2 purity tech will enable you to get purity affinity level 5.
The hidden synergy here is that scavenging should catapult you in science, provided you have lots of aliens to beat up. This means getting tier 1 and tier 2 affinity techs significantly quicker (scavenging makes almost no difference in tier 3), so you can push pretty much any early game strategy sooner rather than later. It is also nice to go purity with this strat since level 3 purity gives you another large combat bonus against aliens.
And here's the kicker -- Martial meditations (right below adaptive sciences) will give you a free boost to any affinity. Meaning you only need to get to level 12 in your chosen affinity.
Other things to note --
Memetwork -- This let's you build your victory building at level 12, not 13. If properly combined with Martial mediations, you can start building your victory building when you hit level 11 affinity (jumping from 9 -> 11 with a single tier three affinity tech is easy with Adaptive Sciences). Memetwork requires orbital networks, which is required for the purity and supremacy victory. Also lowers the affinity level for all units and buildings by 1, meaning bigger, better units sooner.
Ansible gives an additional +25% affinity from techs, possibly giving you +45% affinity from techs. Downside -- it's WAY out on the tree, so by the time you get it, you probably haven't many affinity levels left to get. I hope I can swipe this from the steal tech espionage mission.
And, if you choose, once you get to Eudomonia (whatever, the -15% unhealth virtue at the bottom of prosperity) you can start filling in the bells and whistles in Might like -50% unit upkeep, +

and +

from stratetgic resources, +50% all strategic resources, +% to

per unit tier. And then go stomp people.
Opportunity costs --
First, it only works well when you A) have plenty of nests nearby for alien spawns and B) don't care about eliminating the aliens. Therefore, it's not a very good harmony strat.
Second, and this seems obvious, you will get your second and third cities up later; however, this opportunity cost is more than covered by killing a single alien every turn as far as science goes.
Third, and again this seems obvious, the aliens will probably despise you. A good way to mitigate this is to NOT sack their nests. Nests give a nice +60 beakers, but so do six wolf-beatles. No nests = no wolf beatles. Clearing nests gives a massive penalty to alien reputation.
Fourth, money could become a problem. You'll probably need a large army to clear all the aliens. Recommend getting thorium reactors and choosing +2 energy quest bonus ASAP.
Fifth, by going into might first, you'll delay the awesome health benefits in prosperity. This means staying "tall" longer and not changing to "wide" sooner. This is only a problem if someone settles those cities spots you were looking at. If people don't settle them (this strategy is only good IF you have a lot of aliens afterall), then you don't really need to worry. However, if people do settle your prime 4th, 5th, etc. spots, this problem is easily corrected by you being at level 5 affinity MUCH sooner than the other players. This means you have level 2 of all the basic units (including boats and missile rovers). And you can also have the affinity-attached infantry unit (battlesuits and whatnot). Hopefully, you can just raze and resettle the spots without much difficulty.
In conclusion, this is my go-to strat if I see a lot of aliens/nests close to my landing spot. Basically, it's my go-to strat when going straight prosperity doesn't make much sense (early settler means nothing if there's nowhere to settle). As I mentioned above, it can do quite well with purity. I think this is appropriate because purity has the worst affinity-victory but benefits from Might the most (you can just spam units that move super-fast and aren't affect by terrain). That being said, I think this is THE purity domination strategy.