Really?
I tend to aim for 100% Janissary infantry ASAP in my Otto games. The extra reinforcement cost can hurt early game, but only while in big wars. After you've switched your main trade city to Venice and have a decent amount of control in the node you should be swimming in money so then that isn't even an issue any more.
The military power cost of them isn't an issue. Military points are the least useful ones, you're going to have more than enough to keep up to date, or even ahead, on military tech. Manpower isn't usually an issue so devving manpower isn't that important (plus I don't like doing it in provinces with good trade goods since it'll increase the cost of diplo devving if/when I have excess dip points, so why not use some spare mil points on them?
And they are better than regular units. -10% damage received may not sound like much, but every quality bonus you have makes it easier to beat enemies. And the more you can stack on top of each the more space mariney you're going to be! Plus the double drill gain can be useful to make use of drill bonuses despite having minimal time to actually drill due to near constant warmongering.