I really don't mean to sound rude but I feel I must correct you on many aspects of your op.
1.) No it doesn't. Regardless of the level you play at, you should plan your victory condition way ahead, usually at the very start of the game, and get there as quickly as possible, without diverting into unnecessary techs. The longer you hang around, the better chance an AI has of winning. Also, you can easily destroy AI GDR without having them yourself (see 3.)
2.) A recent patch gave a diplomacy penalty for nuking a civ, though nukes do not cause global warming. Unlike Civ IV, there is no global warming mechanic in the game. You really should use all uranium for nukes, unless you have loads of it (maybe if you play as Russia), in which case you can build some Nuclear Plants in your best cities. Never give or sell uranium to an AI, they can build nukes with it and these units don't suffer from the lack of strategic resources penalty.
3.) GDRs are no where near unstoppable. Their high strength gives them an advantage in open combat, but a highly promoted standard unit (such as mech infantry) can stand up to them well. In fact, any unit can kill a GDR due to the minimum 1 damage rule, where all units involved in combat take at least one damage per round, regardless of the strength of the units. A Spearman will always cause 1 damage to a GDR when in combat, even though the Spearman will almost certainly die. Therefore, you can grantee killing a GDR by suiciding any ten melee units into it. Its even easier than that though, as the 1 damage rule also applies to ranged units such as Archers. Indeed, 10 Archers can kill a GDR between them in one turn.
The problem I find with the GDR (and tanks vs riflemen) Is that they always take one damage even if they crush their enemy. I understand this is for balance but honestly, what are a bunch of riflemen going to do against a tank?
Worst part of civ 5 >.>
With a high enough combat ratio, units become unkillable via melee (though any ranged attack will kill them). A defender with about 3.6x the strength of an attacker (such as infantry vs pikeman) will always do at least 10 damage and and take at most 1, resulting in the defender always surviving.
To me, that's exactly what would make it unacceptable. Trying to pass off giant mechs as a realistic future tech development would ruin any sense of realism. Mechs are for space fantasy games that can get away with positing that such a militarily stupid idea would be used in the far future just because it's cool and sells Transformer models to the kids. A game that includes mechs scores points in my book by lampooning the idea in the process; for a game like Civ it's essential not to treat it as a serious inclusion for the reason above.
A game that wants to maintain a semblance of realism in a future setting doesn't use giant walkers - look at Alpha Centauri.
It is pretty clear from recent history that if there was going to be one more unit in Civ at the end of the tech tree it should be the unmanned aerial drone.
In 20 years the airforce will barely be using any pilots.
Wait, really? Every time you attack you take 1 dmg in this game? How is that remotely realistic when it's bombers versus pikemen?
hehe or when you bomb a pikeman with your B17 and take 1dmg. Those were some long ass pikes!