A lot of larger companies will switch you to an H1-B at some point since they're trying to put you on a Green Card track (bc of long-run costs? not sure). While you technically can apply for a green card on TN status, since TN is intended for temporary workers, it's frowned upon by DHS and immigration departments at companies know that.
Source: I'm a two-time Canadian > US TN-to-H1B and eventually bailed out of the process by marrying an American.