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I don't own an iPhone so I don't know for sure if old messages clog iPhones too but the article hints that this is the case.It really depends on how much people send you photos and video. Text is not going to be much of an issue.
I have a SMS/MMS/RCS backup that spans ~15 years, and it (uncompressed, with media files base64'd) is 1.6GB. MMS compresses media files to the point of garbage before sending them, so a more modern app would end up with (much) larger media files. My Signal backup file is around 2GB now; I'm not sure if it's compressed (probably?), and I've been using Signal for a much shorter time and with fewer people than SMS/MMS/RCS.
(The irony is not lost on me that I am the kind of "offender" that the article's author talks about, someone who keeps messages forever.)
For a modern decently-high-end smartphone with 128GB of storage (or 2x or 4x that), I don't think this amount of messages would "clog up" anyone's phone. But maybe it could be an issue for people with budget-oriented phones that have less storage.