We have a Succubus in our party (DM allowed homebrew races) and the mechanics of its shape changing ability have come into question. Our DM noted that the word "polymorph" is used in the explanation of the Succubus ability, and that even though it isn't underlined, it refers to the spell. And following this (IMO logically false) premise, the Succubus should follow the other restrictions of the Polymorph spell, minus the exceptions clearly stated in the Succubus Shapechanger ability blurb.
I contend that the word "polymorph" in this instance is simply being used as a synonym for shapechange, and that it has nothing to do with the spell. Firstly, Polymorph only allows for changing into Beasts; this allows for humanoids only. Polymorph changes half your stat block; this changes no stats. Polymorph melds your stuff into the new body; this drops everything. Polymorph is a spell, and in other instances of it being bestowed as an ability (for example the Warlock invocation) it says, "can cast Polymorph" in its noun form; this uses 'polymorph as a verb' with no mention of a spell, components, duration, targets or saving throws.
I mean, it's still a cool ability, but it's not like you're zapping into a new form and blending into a crowd. You would be naked. Having just dropped all your belongings.
The following is just my interpretation. Ultimately, all rules are subject to whomever the DM is and what they are willing to play with in their own games. With that aside, here is what I think:
Polymorph does work as you stated, however you would not drop your belongings as the spell states all equipment melds into your new form. There are a few ways I would play around this wording. For instance, you can take a note from the druid Wild Shape ability, where "you choose whether your equipment falls to the ground in your space, merges into your new form, or is worn by it." It isn't game breaking and still functions the way the player in this case seems to want to run it.
If the player is using it abusively it then falls to the DM to figure out a balance of power. It can be something subtle as not being able to change your fiendish eyes or claw like nails. Something that still allows a creature/humanoid with high insight or perception to figure out what happened.
If it were my game I would have offered the changeling race as an option to the player instead of creating a homebrew succubus. It is difficult to find a perfect balance and the changeling is already there with options to disguise yourself as an action whenever you may need it.
I would not treat it under the same rules of Polymorph... the wording for the ability is imprecise since it's written for a monster where the specifics of the details don't really matter as much. I think it makes more sense to treat it under the rules of Alter Self, rather than Polymorph.
The ability doesn't reference the spell in any way, much like many effects that cause something to become invisible do not reference the spell invisibility and thus are not subject to the restrictions of that spell.
The polymorph spell specifically changes the target into a beast, so restrictions on speaking and casting make sense. The shapechange ability is limited to humanoid forms only, meaning zero overlap in available forms.
If they DM is concerned about the potential for abuse, have them look at the changeling race, or, if you don't have access to that, at the warlock invocation mask of many faces.