If you climb at a constant AoA for finesse max, the wing will be happy but the engine will not. As thrust goes down with altitude, Vymax changes slightly for a good balance between maximum wing and maximum engine performance.
A climb could be scheduled as function of AoA, but it is not going to be more or less effective than scheduling it as function of indicated airspeed.
There is also the accuracy of the measurement/indication that would be involved. AoA is rarely indicated in tenths of a degree (let alone calibrated), which equates to changes of only one KIAS. So when deciding whether AoA or airspeed is the better source of information for climb performance, the latter has an advantage in terms of accuracy. That would particularly be the case if your AFM climb schedule has weight as input parameter.
For stall avoidance, AoA indication is king. But as a tool to get best performance, IMHO speed is best.