I don't ever recall anybody bothering to ask application developers
whether it was okay for DHCP servers (much less NATs) to break open
connections.
This is a bit of a red herring--as actually implemented, most DHCP servers
provide leases long enough that your IP number doesn't change unless you
lose connectivity for a while, in which case the connection will usually
break anyway.
Many ISPs routinely use DHCP as an means to degrade their customers'
address stability, forcing them change addresses as often as once a day,
in order to prevent their customers from running certain kinds of
applications.
Keith