TN can be extended indefinitely, so if you're being pressured to change to a H1-B you might want to ask why until you get a direct and specific answer.
TNs could be renewed indefinitely, however they're specifically meant to be temporary so you can only renew them if you continue to convince the adjudicating officer that you do not intend to renew them indefinitely. This may become a challenge a decade or two in. They are explicitly not a replacement for a green card. They can also be revoked at each border crossing.
An H-1B gives you a defined 6 year window with doctrine of dual intent allowing you to pursue a green card, which a TN status does not.
