I've recently begun to study Kalaallisut (Greenlandic), a language frequently described as polysynthetic.
Among other things, I am struck by how little I have found Kalaallisut surprising or hard. If anything, it feels very Uralic; while there are elements that speakers of European languages will understandably find difficult (especially uvular consonants), the grammar feels incredibly straightforward — there are morphemes, with clearly defined meanings, and you string them together to form words.
Now, some of these morphemes have meanings that you will not find in European languages. There is, for instance, a bound morpheme meaning 'to eat or drink <noun to which it is added>', which is not something that Finnish, English, or any other natural language I have studied has an analogue to. However, there is really nothing particularly strange about this morpheme — you learn it, you learn the rules about how to use it, and you learn what it means, and that is that. And so far, the sentence and clause-level syntax of Kalaallisut also seems very familiar, although we have only seen so much of it.
I understand that I have a background in linguistics and have studied dozens of different languages, and should not compare my experience of learning a language to that of an absolute beginner. I nevertheless find myself wondering how useful the concept of a "polysynthetic" language even is, given how blurred the line can feel at times between an affix (or element of a compound) and an adposition or other independent word that triggers sandhi.
None of this should be taken to mean that "polysynthetic" should be abandoned as a category, or that languages classified as polysynthetic are not different in categorizable ways from languages like English. However, Westerners have an unfortunate tendency to exoticize languages that do not work like their own, and I worry that some of this has leaked into linguists' and especially conlangers' concept of what polysynthesis means. I also sometimes worry that people overestimate just how deep typology goes, and mistake certain language classifications for something more mystical than just "there are long words with lots of morphemes in them".
At some level, all languages are just collections of pieces and rules for how to put them together. It is important not to forget this.