It's not necessarily an equalizer. The rich can get richer or the poor can get poorer.

I'd rather say, Muslims have other incentives. Like, when they build a waqf, it's for the akhira (and hasana jariya). When they follow the rules (including the Sunnah) of zakat, their economic behaviour becomes a means for both, a better akhira and dunya. Because even the rich profit from an environment where the most needy are taken care of. But it doesn't necessarily make them less rich.