Not popular to eventing due to the fact of being a rare breed outside Portugal...the Lusitano (that is under my nose all the time) is just perfect for eventing!! Very very brave, inteligente, easy to train, loves to please, athletic, very hardy and with great stamina...and it comes in different sizes (Veiga are smaller but very very strong with great moves....very much used in bullfighting and Andrade...bigger...heavier...crosses between these 2 lines are very useful and popular in Portugal).
I wish I had some video of this little Lip. Pony! (I tried him out when I was trying horses) He was a really nice horse(WAYYYYYYYY out of pricerange!) and he bit people, which was a deal breaker for me anyway
I'm getting into the lower levels of eventing on my Arab/QH cross. He's 3/4ths Arab, 1/4QH and he's extremely athletic though I doubt he'll be going up too high. But that's getting way ahead of ourselves. We're still newbs to it but he's a very brave, honest little guy when jumping and can hold his own in dressage so he's looking promising.
Everyone I know who's doing higher levels has a TB or a TB cross. The only down fall I could think of with a TB's physical soundness is they are usually started extremely young and already have had a lot of stress put on them physically before entering their eventing carreer.