No, because conditions have changed markedly. For metals to act as catalysts, and replace some metabolic enzymes, they need to be in highly reduced conditions. This was true in early Earth, but about 2.5 billion years ago, we had the great oxygenation event, and over the next billion years free oxygen has gone up enough that you won’t find the reduced conditions where metal can take over the job of metabolic enzymes in much of Earth anymore.

That is, what sustains today’s life prevents new proto-life for forming. You need to have the fancy gadgets life has today to continue to survive and replicate on Earth.

Note though, it was other life forms that contributed to the great oxygenation event, too. This is all a continuous web.

Coacervates, liposomes, acetogenic precursors, etc are all commonplace and could be considered proto-life. Some scientists have even argued that viruses are proto life. Prions (misfolded proteins that can self-replicate) and plasmids (non-chromosomal DNA strands that play a major role in horizontal gene transfer) are also candidates for proto-life that blur the line between living and non-living

For what it's worth, metals are still critical catalysts all over biology, they just tend to be encapsulated in biomolecules.

I always found it odd that there's only one single origin of life point or even just a single common ancestor considered in history. Shouldn't entirely new life develop all the time on earth? I mean the ingredients and building blocks are still there, the environmental situation still should work out, like availability of water, temperatures, etc. We should see a constant emergence of new life all the time. Why would that process stop, just because some other life already exists? Maybe we just can't detect this, because whatever new life happens to appear —more or less— resembles life that's already there.

Hash competition from life might cause them to go extinct, and even if it happens again it just gets out-competed to extinction fast.

Maybe, or maybe it was eaten into extinction.

Geology over large time-scales is profoundly unforgiving.