If you can't save on triggers with the occasional use of a wait, you're probably not using the waits efficiently. WIth waits, you can consolidate actions that go before a delay, the delay itself, and actions that occur after the delay into one trigger...and you're not limited to just one delay per trigger, either. This consolidation means they have a higher inherent efficiency in terms of trigger count than death counts (and if you can avoid any disadvantage, even saving
one trigger would be superior to saving none...and it's not at all hard to save more than one trigger on a single occasion, let alone in your map as a whole). Personally, I find that a well-placed Wait 0 is often the easiest way to solve problems relating to the different update rates of Starcraft conditions...just put it in the right spot and the problem is gone, with no other changes required.
Death counts may be the most suitable system to use as your main method of timing, but that does not mean that you should neglect other systems. For instance, suppose you have a map where the player can buy multiple reuseable healing items that will repair him, and you want to set up your map such that each one has its own independent cooldown (so for instance, if the cooldown is 10 seconds, and the player has purchased 40 of the healing item, he should be able to heal four per second continuously, because the cooldown for the first one will finish 1/4th of a second after he uses the 40th one, the cooldown for the second one will finish 1/4th of a second after that, and so on. Of course, because the effect that you are trying to simulate is each item having its own cooldown, there's no reason why the player should have to use his 40 healing items in nice, neat 1/4th-second intervals.) Now, that's just one item type: suppose your map has not one but 10 types of item, each of which allows each example thereof to recharge independently of each other item that you own. If you were to handle the timing in this situation with death counts, the fact that each healer, each exploder, each teleporter, each
whatever is recharging based on a timer that is only answerable to when
it was used, independently of others of its kind, you'd wind up with a mess, especially if there's no limit to how many items of each type the person can buy. On the other hand, if you were to do things the way it used to be commonly done, with each different item's recharge based on a unit (usually air) moving along a track of set length, you could handle hundreds of different independent rechargings with just a handful of triggers.
What I'm trying to get at is that you should always try and use what is best for your situation, not necessarily what is best 99.9999999% of the time, even if the system that is better 99.9999999% of the time is only 0.00001% worse in this particular case. Death counts are the best timing system most of the time, but sometimes you can get slightly more efficiency with a wait, or a moving unit, or some other alternative form of timing. Don't be afraid of doing something the "wrong" way if that way is right for your map.
None.