You will find that if you call the hospital when your water breaks, in most cases they will tell you to come straight in.

There are no pregnancy police that are going to come and get you though if you don't

The risk of infection is actually pretty miniscule in your own home where your body is already colonised with the bacteria that are there. This is not the case in hospital - which also has a heck of a lot more bacteria than your house, and where there are people wanting to put their fingers in your vagina as soon as you get there...which is the first big no no in minimising infection risk

If you go in as soon as your water breaks and labour takes a while to get going (which it often does) you're at huge risk of further intervention - ie. drip.