Should immigrants have a path to citizenship?
Not American, and I'm guessing you are using citizenship and nationality interchangeably, so thats the basis on which I my answer should be considered.
As a matter of general principle, no.
Legal residence, work permits, social services, even the right to vote in national elections, or to not be deported for crimes can be up for discussion.
However, a nation state is just that, a state that does not exist for the benefit of any despot, nobility, or priesthood, but rather consists of a nation (people/tribe) by it's own sovereign mandate. If you are a member of the nation, you are then by definition a national with a nationality. It doesn't matter what any politician, judge, or code has to say on the matter. In this the highest authority is reality itself, closely followed by the tribe.
As far as Im concerned, the only way to become a member of such a tribe is to be born into it, adopted by one of it's members, or by the members voluntairly merging multiple nations into one. Once achieved, membership is permanent and non-negotiable until such time as the tribe is dissolved. While you yourself may renounce your nationality, other members of the tribe cannot take away your membership regardless of law or custom. It is defined not by these, but by who you are.
There is however a big however.
All the rights and obligations of a member of the nation (i.e. a
national) may be granted by
citizenship which can be issued to a non-national, and this is not quite the same as nationality. The reason these are not the same is that citizenships are a legal construct that may conceivably be edited or revoked. But this is unusual enough that most people don't really distinguish between them. I consider it an important distinction though.
Once the previous long-winded distinction is made, I'm persoanlly fine with there being a path to citizenship as long as there is a reasonable threshold for revoking it.
Not stuff like getting drunk and getting into a fight, getting a speeding ticket, or getting your taxes wrong once or twice, but actual serious criminality, hatred or gross disloyalty towards the tribe harboring you, being a drain on them, etc. If you are a contributing you are welcome to stay, and if you have kids with a national, they automatically become nationals with non-revokable rights as well, so congrats on that.