Is Offering to Memorize a Surah as Mahr Problematic?

Absolutely it is problematic. Mahr is supposed to be a reasonable social value amount. It should not be exorbitant on one extreme, and it should not be reduced to a hollow gesture on the other.

Men who quote the sahaba in this context — did you find one story that you want to hide behind, or did you find the whole picture? The sahaba who were in those situations were bankrupt because they were serving the mission of Allah's Messenger ﷺ. They had lost their homes, lost everything, were in desperate conditions while carrying out a mission we will never face. To use their context, which you are absolutely not in, to justify avoiding financial responsibility to someone you are asking to build a life with you — that speaks to a fundamental lack of understanding of both that context and the Quran's concept of qiwamah.

Men are supposed to take financial responsibility in the Quran's framework of marriage. That does not mean women take financial advantage. But it does mean that "I'll memorize a surah" as your entire contribution is not an acceptable substitute for that responsibility in our current circumstances.