Spore makes use of some incorrect biological premises. However, it's all for the sake of good gameplay.
Creatures in Spore evolve by spending earned DNA to develop new body parts. In a very general sense, this is a decent representation of how real species develop different traits over time.
However, Spore ends up confusing modern evolutionary synthesis with Lamarckism, which has been disproved.
Essentially, Lamarckism is the the concept that individual animals who use a body part more than other individuals will have offspring with a better version of that body part. For example, if a gazelle tries to run faster than other gazelles, then Lamarckism states that that individual gazelle's offspring will be able to run faster than other gazelles.
This is how Spore gameplay works. The body parts you are most likely to discover through play are the upgraded versions of the parts your creature already has.
However, that's not how evolution works. A population of creatures (like gazelles) will have a variety of genetic traits that they have acquired over time through random mutation. There are all kinds of traits that individuals in a population can have (like long and short legs), and those traits can be good or bad, depending on the situation.
If cheetahs attack our gazelles, the shorter-legged gazelles get eaten because they are slower, and the longer-legged gazelles survive to breed. The next generation will have longer legs.
Evolutionary pressure doesn't happen like this in Spore. If you die, you are reborn with the same features you had before. Whether your creature gets chewed on by a sea monster or outruns an angry troupe of freeps, your creature's next generation doesn't get tougher skin or a better run speed.
From a gameplay perspective, though, would "realistic" evolution be fun? Probably not in Spore's context.
Pre-tribal gameplay is already rather low key. Basing new body part choices on what features allowed you to survive (or die) might result in the same Lamarckian options. Removing part collection would take away perhaps a third of the game.
On top of that, if you earned DNA mutations at a steady rate, all you'd have to do is survive in order to progress - you'd have no motivation to befriend other animals, only eat them.
In the end, the Spore cellular and creature stages probably incorporate the best of both the biological and gameplay worlds.