It is true that the design of OP, such like the target being completely frozen or the effect having an effective time, does not cater to the style of AoE2.
But in the other way, we can refer to the Obuch, making unit attacks change the target’s stats, which can make enemies slower, slower to fire, etc. This may be better accepted. I give this concept to the UU of the potential Jurchen civilization, the flail cavalry.
I don’t like making the Fire Lancer a cavalry unit.
The cavalry type of the Fire Lancer in AoE4, I think it refers to certain artworks on the Internet, and it emphasizes the Mongolian military style as a Yuan Dynasty unit. Mechanically, the AoE4 Fire Lancer is just like a Coustillier + Tarkan + trample damage, no such a fancy shock effect, but even if this design is used in AoE2, there will still be problems.
This weapon tends to be better suited to infantry use. As far as I know, it is indeed mostly used by infantry. In my opinion, the fire lancer is more suitable as a foot unit, and may simply serve as a predecessor to the Hand Cannoneer, without a fancy gimmick or particularly powerful effect. In this way, it would not affect the balance of the existing civilizations too much.