Dumb Question of the day about Cordless Phones

I can't see any reason why it would. We have what would now be termed an old-fashioned push-button telephone plugged into the kitchen jack. There is no call display or anything, just a plain phone. Then we have a set of 3 cordless. There isn't any interference so I don't see why getting a different cordless phone would make a difference. The features may not work together. For example, when one of us is on one of the cordless phones the display says "line in use". But if someone were on the phone in the kitchen, it doesn't say that. You'd be using a phone with a different base so it wouldn't jive but shouldn't interfere as people have many different types of phones in their houses and they don't interfere with one another (for example a superstar who has a 15 bedroom home which probably has at least 20 different phones in it ).