You do not have to give up US citizenship to get UK citizenship; you can have both.
The biggest advantage of UK citizenship is (somewhat sadly), always having the ability to live in the UK. ILR is only valid so long as you remain in the UK. If you're away from the UK for 2 years, ILR is lost and if you wanted to move back, you would need to qualify for a visa and start from the very beginning again. As you never know what will happen in the future (and IMO, especially if you have elderly parents back in the US who may need your support later in life), it's probably a good idea to get UK citizenship so you know you'll always be able to return to the UK regardless of how much time you spend outside.
There's being able to vote - which I wish was the bigger attraction rather than not potentially losing ILR. And at least still right now, you can benefit from the UK's remaining time being a member of the EU.