Harmful trees?

Does anyone know how these strange (tropical?) trees are called? The photo has the baby version, got big ones around the house.

Well, that gives me a flashback to our sewer line replacement at my mom's house in 2020. The first picture shows a tree in the foreground that gives me plumbing nightmares. We see them on our walks along sidewalks that are completely torn up. 

Having worked with arborists as a board member of a HOA. I can tell you that people don't make wise choices when planting near homes or water lines. The developer even completely messed up the landscaping and you would think a developer would use an arborist for landscape design.

Can't really offer any insight here, but the landscaping looks beautiful. Shame it's affecting the property negatively. 

Thank you all.
We checked Yucca Gigantea and Cordyline australis on google images, but they look a bit different.
I think I have some Yucca Gigantea in pots and other locations (so many plants!!)
But the big ones in my 2nd photo that I have everywhere are a bit different, they have a dark edge on their leaves and several branches. The branches are very flexible by the way, I'm sure they will break if I push them down.

I lifted some 4 year old laminated flooring in the basement today, and guess what, thin roots under the laminated! These plants are super invasive. I just need to know which ones to take out. I read that some palm trees have horizontal roots like that, that extend 20 meters horizontally, but are weak and don't damage buildings, but can go into plumbing. New country, new problems 😀