|Don't ask to ask, just ask|
In the old days of the WWW, AOL users were forced to use HTTP proxies provided by AOL. The setup had the annoying feature of using a different proxy for each request, so that the requests from a single user appeared to come from a large set of very different IP addresses, while each single IP address was used by a large set of users. Websites that assumed constant client IP addresses were unusable, websites that assumed one user per client IP address had huge security issues. I don't know if AOL still uses this setup, things have changed a lot since then. But as far as I know, this setup does not violate a single RFC, and websites that can't handle this setup are broken, period.
HTTP Proxies have become more and more popular, especially in corporate environments; mainly for security and for filtering / censoring unwanted content (mainly malware and porn sites). Many mobile internet providers offer a low cost connection that uses private IP addresses for the mobile device and a forced, transparent HTTP proxy to reduce the data volume in their mobile networks. But unlike AOL, they seem to use only a single proxy, or at least try not to change the proxy during a dialup session.
Big internet providers have several IPv4 address pools, simply because they had to request a new block from time to time. Those pools are not continuous, but fragmented. Dial-up (and DSL) clients get a random IP address from the pool, and with each new dial-up, the IP address may change wildly. Some providers use several small regional pools with perhaps two, three or four IP ranges, some have use a large common pool for the entire state with a large number of IP ranges.
At least in Germany, DSL connections are disconnected after 24 hours, and usually, the IP address changes after the reconnect. Fixed IPv4 addresses are available for extra money.
Today I will gladly share my knowledge and experience, for there are no sweeter words than "I told you so". ;-)