Most ults are ready every fight it seems, is this good?

I feel like ults cool down in general are way to quick. There is hardly any window where you can engage a champion who doesn't have his ult ready. Annie, lux, trynd. Ask yourselves really how many time a fight breaks out and their ult is not ready. Whats the point of cool down if ults are ready at every significant team fight? Where is the punishment for poorly choosing when to ult and squandering it recklessly?

Furthermore, if ult cool downs were much higher across the board on all champions, there would be more depth to managing your ult as you will not be using it as often as before, and allow players to create more situations that take advantage of their ults being ready or the enemy team having burned their ult last fight and they are still on cool down.

I know this doesn't fit with the frantic stupid cool hip hop style that league is always moving closer to, what with the crazy fast action and plays that look cool to watch, and it definitely would make LCS more boring to watch, but I would enjoy that game more.