Is it really worth building my strongest units?

Seriously, I don't know.

I thought building my strongest units basing on my civ would be useful to win noobish games on <1200 rank on Voobly. But this doesn't seems the case.

For example, I just ended another game on noobish <1200 BF.

I was Maya and so I built my strongest units (Elite eagle warriors and Elite plumes). Then I attacked my opponent by minute 35.

But as soon as I destroyed my opponent palizade, I found to wait me Hand Cannoneers, Huskarl and Two-Handed Swordsman. All units that are strong against my units. And this happens every single time. I focus on building my strongest units while my opponents focus on building my counter units. So I guess I should start building counter-counter units? What's your suggestion please.