Same reason we bought when we did. Our kids were a year or so younger than each of yours when we bought, but after a couple of years of looking we decided they weren’t getting younger and we needed to go ahead and do it for them to enjoy it. If school’s out for more than a couple of days, they are at the beach house. It gets them away from all the bs at home and let’s them have time with each other and outside. The summers get a little long, so the last two years we have brought them back home for 2-3 weeks in the middle to see their friends and do other things which makes everything go better.
As others have noted, the costs are what they are so make sure you can afford it. Insurance and taxes keep going up, repairs are a constant, utilities and other things are always there, we have someone check on it once a week while we are gone which costs something, etc. but for us it’s worth it.