Relative plenitude did not dictate the elements we and our relatives use, and would not for other life, either. In any case, many other elements are plentiful.
Carbon is a good choice for our temperature range, but there are plenty of temperature ranges as well or better represented. Life will not sneer at the others. Most life on Earth cannot make any use of the carbon in CO2, no matter how much of it there is; in fact, the more of it there is, the worse off most living creatures are, only green plants excepted. You would die in a room with the nitrogen replaced by CO2, despite that you use none of the nitrogen at all. (Only bacteria can "fix" nitrogen, and only some of them.)
Iron is very plentiful in the cosmos and in Earth's constitution, and most life depends on it, but it is practically nonexistent in the open ocean; yet life thrives there. Even where iron is plentiful, life uses hardly any. Silicon is extremely plentiful, too, yet used by our life even less -- until just lately!
So, your argument from plenitude utterly collapses. Life as we know it is a product of history and circumstance. Given different circumstances and different history, you should expect a different product. There will certainly be similarities dictated by physics: e.g., cells are very, very likely, and equally so use of liquids. Aperiodic fibers to encode genes, cognate to our DNA, and others to fold up and carry out processes, cognate to our peptide chains a.k.a. proteins, are quite likely. But there is no reason to imagine that any of the details of the encoding would match.