Several thoughts for quick speed:
-you always has bad start and have no time to walk around finding better
-barbs count is increased, sometimes you may need 2 archers just to clean barbs on your land
- Investing in units simply means that you delay expand a lot and will loose perfect locations for cities (like natural wonders etc.) and you often missing production. (my usual BO is scout-scout-shrine-settler and this is faster then liberty settler, add here archer and it can be slower than liberty settler)
-first politics in tradition is useless at start, if u build monument in cap - second is fairly useless as well. And with honor you wont delay 3-5th politics.
-you will be slowed in politics later, but I think compensation is great. Again on quick speed you do have much less time to transfer units, so u basically clean barb camp with what you have here and now. And again clearing camps are harder on quick.
-And again 1 general is often enougph to cancel attack on u or to take one enemy city.