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1) Further on the words of Maharal, in regard to the Jewish monarchy, it it important to recognize that the prime function of the king was to protect the workings of the society, namely, for example, to fight the necessary wars and/or maintain, law and order. It is, as such, important for the Jewish king, in regard to these secular functions, to also reflect strength and permanence, It is within this Divine task for the Jewish monarchy that we do, indeed, refer to the Davidic dynasty as the House of David. It is, though, further important for us to recognize that this is still indeed part of its Divine task -- it is the Divine that demands this involvement in the secular.
At the same time, though, we must also recognize that the Jewish monarchy's role is also intended to extend into the religious realm. It was still the project of the monarchy -- in specific terms, the dream of Dovid HaMelech finally brought to fruition by, his son, Shlomo HaMelech -- to build the Beit HaMikdash. It is in this recognition of the Jewish monarchy's purpose beyond the secular that we refer to the Davidic dynasty as Succat Dovid.
2) Further on the words of Malbim, it is interesting to note that his perception that the coming of the Mashiach will occur in an incremental manner would be in line with -- although not necessarily in specifics -- the modern perspective of Messianic Zionism as presented by such individuals as the Raya Kuk. Rav Kuk's argument that the return of the Jewish People to Israel, even as spearheaded by the non-religious, was the beginning of the Redemption, also reflected an idea that the coming of the Mashiach would be in an incremental fashion although, obviously, not similar to Malbim's perspective of this incremental process.