We had a cat (lovely tortoiseshell who came to us as a kitten with knock on effects of severe early trauma) when I was growing up, and I had a cat with epilepsy (and one dog, and then 7 dogs...) when I lived overseas and I'd love to have another cat.
I am pretty sure my DCs would be enchanted by the idea (they are 5 and 3). We have just moved to a new larger house which has less carpet and has a ready made cat flap.
We would be more likely to consider an adult cat (I thought about a kitten when I was on leave with DC1 and then again with DC2 but we are both out at work at least 2 days a week so it's not really fair on a kitten I know - I think when we had ours my DM was out at work but things have rather moved on since then I know).
But DH is somewhat allergic. He tends to become wheezy/headachy when we visit cats.
I am not sure there is a solution to this problem! We are part time cat feeders to next door's cat - but we can't really become cat aunties/regular visitors most of the time as they also have vvvvv large dogs and my DC2 is smaller than them (as is frankly my DC1 and possibly me also) and terrified. (Dogs go on dog holiday when NDNs go away).