Some (Fruit) trees have to mature a few years before they can flower and cary fruit. Palms are one of those, some need 5 years (Like our Cherry tree) and there are palm species which even need about 50 years. I got one in house standing here for 12 years now and still didn't flower, i forgot the name after all those years. Almost the same as yours but thinner leaves and about 2 meters high now.
When you buy them they are very young maybe 1 or 2 years old depending in what conditions they are grown. Growth under artifical light can be rather fast and can become quite big in the first year and look rather mature, but aren't. 🙂