Do Amps matter.. in an Amp?

I have Magnepan speakers, and have tried dozens of amplifiers. I do find they sound quite different with different amplifiers. Tubes, class D, and A/B may be where to see some trend but lately I’m stuck on amperage. Most product tout wattage, which I find misleading since the highest wattage amp I own has the least satisfying sound. My favorite amplifier claims >60 amps of current, and a few manufacturers state this measurement. But most don’t. Is it significant? What does max amperage mean compared to the damping factor or the wattage change into different loads? Seems like an easy engineering question but I don’t see it discussed very often.