'Need' is highly subjective. I think the two reasons you posted - shorter brew day and less chance of infection - are good reasons to put a wort chiller in the 'want' category, if it makes sense for how you brew.
For a 2.5 gallon batch, I don't think it even falls into the 'want' category any more, though. That small a batch will cool down fast enough in a sink of water that the investment in a chiller probably isn't worth it.
Now when you're talking about a full boil with 5-6 gallons of hot wort, it becomes more useful. That can take a very long time and a lot of water/ice to cool. Plus you have to lift all of that hot wort into a sink, which can be dangerous.
No-chill is certainly an option, and a good one. It's not for everyone, though. I don't like sticking my hot wort in a plastic container, and it becomes problematic at larger volumes - I'm doing 10-15 gallon batches, so I'd need a lot of intermediate containers, or large (read: expensive) ones.
I just want to go from kettle to fermentor, and a wort chiller allows me to do that in a reasonable amount of time without lifting heavy pots of boiling liquid. That right there is worth the investment for me.
Speaking of time, a bit off-topic, but a pump was mentioned. Using a pump to recirculate the wort while chilling has made a huge difference in how long it takes to chill down to yeast pitching temps for me. All of my boil kettles now have recirculation ports so I can recirc while I chill.