Not at all, you're presuming there are many different ways life could work, that might not be the case at all. It's entirely possible there's only one or very few possible recipes for life so no matter how many abiogenesis events occur, they produce the same kind of life.
A simple analogy, wood burns, fire is fire, you don't expect every different occurrence of fire in nature to produce a new and incompatible type of fire. Life could be the same, it could be that anywhere carbon based life forms it's basically the same basic recipe and thus biologically compatible with all other forms of carbon based life.
Presumably this is even MORE likely if the independent lifeforms both emerged in similar physical & chemical environments.
https://en.wikipedia.org/wiki/Great_Oxygenation_Event
The vast majority of life on Earth has been wiped out simply because other life created inhospitable conditions for them. Even if multiple events created life, if the wrong life is created, it will die.
A universal common ancestor does not imply that there was only one organism at that time. All humans share a common female ancestor dubbed Mitochondrial Eve. [0] She was not the only woman in the world when she was alive.
Since the primordials soup times, we also have energy hitting inanimate matter. On this planet. And also we have the other planets in our solar system. Why aren't we finding lots of bacteria being spontaneously generated everywhere?
It isn't that a novel form of primitive life arises then gets eaten; the building-blocks necessary for a novel form of life to arise get eaten before those building-blocks have much chance of interact at all. From what we can tell it would probably take many millions of years of chemical interactions in the appropriate conditions after being seeded with carbon-based molecules from comet/space impacts (since carbon compounds seem to be relatively common).
It seems likely that life will spread and adapt somewhat quickly since it is usually easier to find new resources than enter an arms-race over existing resources. That leaves a very narrow window of time (in evolutionary terms) for life to arise >1 time independently then evolve enough to be on equal footing with the other form(s).
It also seems far more likely that if this very rare event takes place one of two things happen: 1. One form of life has a head-start in the arms race and overtakes the other, completely wiping it out 2. The two forms of life are compatible enough to exchange genetic material because they evolved from the same raw building blocks deposited on the planet; though it mostly fails to produce viable offspring in a few cases the forms successfully cross and the new third form of life successfully outcompetes its progenitor forms.
As for Mars, it seems likely that life never evolved there at all.
The next best explanation seems to be life never got beyond single-cell organisms and struggled to eek out a short existence. Before Mars dried out and/or the massive hemisphere-shattering impact struck and erased what traces of life once existed.
The simplest bacteria today are amazing organisms. They have cell membranes, which separate the protoplasm of the cell from the outside the world, and only selectively let some molecules through. They contain a blueprint to produce catalysts for a variety of chemical pathways; they can store energy in chemical form and use that energy to catalyze these reactions. The can break down complex molecules into simpler molecules and reuse these building blocks for their own purpose. They can move, to seek out new food sources. They can produce toxins that interfere with the chemical pathways of other cells, killing them.
But when we talk about abiogenesis, we aren't talking about the spontaneous generation of a cell. We're talking about the spontaneous generation of a single molecule, or a small set of molecules, probably proteins (amino acid chains) that, in the presence of proper raw material (amino acids) will tend to act as a catalyst for the formation of more of itself.
That's it; the reaction does not even have to be fast or obvious, even. If it takes years for the molecule to catalyze its replication, that's fine. Everything on top of that comes down to evolution, the slow development of a new trait - cell ways, a genome separate from the cell machinery, the ability to metabolize organic molecules into raw materials, locomotion - over millions of years.
So in addition to xenadu's point, there's also this: the abiogenesis of new self-replicating molecules could still be happening today, and we'd probably never know. The objects in question are too small, and the time scales involved are too large.
It depends on how you define life. If viruses are a life form then you have one. If self-replicating meta-structures composed of multiple different species interacting such as lichen count as separate life forms made of other life then that might count too.
On the more far-out side of theoretical biology people have proposed culture/memes and the modern high-tech economy as a new form of life that has emerged from previous life. If solar power (or fusion) becomes ubiquitous and it learns to recycle nearly all its waste it will become an ecologically self-sufficient form of life, and if AI ever gets good enough to have machines designing and producing machines it could "fork" and become a completely independent form of life.
This makes sense. Life exists here on earth, I believe it got here through natural processes, and so it seems that life should be expected in the right circumstances.
But this begs the question, has life arisen independently from other existing life in the last 4 billion years? All known life shares the same fundamental genetic code and appears to descend from a single common ancestor. Are we to believe that the founder population of all life on earth, from which the GCA hailed, is the only instance of life on earth arising directly from inanimate matter? Or has life arisen independently between 4 billion years ago and now, just to be out-competed by existing life forms? Or were conditions just right 4 billion years ago to allow for the spontaneous generation of local-entropy reducing molecular agents (which evolved into life), and ever since conditions have been wrong for the generation of life?