Is there an internet provider that assigns a random ip address when you connect to the internet and disposes of it when you disconnect?
No not really.
You either get a static or dynamic IP. Obviously static isn't want you want. However, dynamic IP assign by dhcp are not random. Each IP in has purchase 1 or more ranges of IP addresses. Typically handed out by region.
There is a dhcp leases, and when the lease expires it tries to get a new IP, however 99% of the time it just gives you the same one back.
When you disconnect, and later reconnect you get an IP from the pool. The range of IP is limited, and way to limited to be called random. Plus some ISP may log these devices.
Disposes, as in never to be re-used by anyone, nope never there are just to few IPv4 left to ever allow an IP to go unused.
Disposed of, as in you never use it again, again IPv4 is too small to allow this. Chances are in you will eventually get the same IP back again.
Now, IPv6 has 2^128 address vs 2^32. You might be able to buy blocks of IPv6 and after you used them once resell them and get a different block. This however, is a lot of work, and records are kept so it wouldn't get you any anonymity.
Also 90% of the internet is IPv4 so if you have an IPv6 nobody on IPv4 can easily communicate with you. They could get a VPN, but your typically user isn't going to do that just to visit your site.
Yes, pretty much most of them.
IPV4 addresses are a dwindling resource.
But if you are looking for a way to hide your identity while you rob banks, then don't assume they don't keep records of who had what when.