There's an extremely simple and powerful reason why neo-Darwinian evolution (NDE) is overwhelmingly confirmed by the experimental data.
Suppose I have two decks of cards.
The first deck is sorted in order of rank and suit (two of clubs, two of spades,...).
The other deck is composed of random cards, with duplicates allowed. This second deck could have been produced in any possible way. It could have been arranged by someone who likes twos, or be left over from last night's poker game, or express the first 52 digits of pi using aces as ones. There are lots of possible ways the deck could be arranged.
At random, I place one of the two decks in front of you. You turn over the first card. It's the two of clubs. What are the odds that I placed the first, sorted deck before you?
The answer (using Bayesian statistics) is about 98%. And it's simple to see why. The prior probability we assigned to the arrangement of the unknown deck was spread out over countless possibilities. Meanwhile, the prior probability of the sorted deck was focused on only one. The "sorted deck theory" was bold and made a firm prediction, and was suitably rewarded.
There is a strong analogy between this and the ID vs. NDE debate. The sorted deck is analogous to common descent. The random deck is analogous to ID.
NDE essentially requires common descent. There might be more than one line of common descent to the simplest life, but it is unlikely that there would be more than a handful. Yet, in any case, every life form must trace its lineage back to the simplest life.
In the case of design, this isn't true. There's no reason why a super-intelligent designer/manufacturer could not have designed moles using non-DNA technology, and without inheriting from any ancestor species. Indeed the same is true for every species. Every species could have been uniquely designed. This means that there are billions of possible permutations for separate lines of descent of species.
Indeed, it was once believed that a designer made all the different kinds of creatures as their own special invention. This is a plausible position given that humans often design systems from scratch, and not every system we build was descended by variation from a prior design on a particular technological platform.
So, when we apply Bayesian statistics to this we find that generic ID is effectively falsified, and NDE is overwhelmingly confirmed. DNA evidence is that all life can trace its way back to the simplest life. ID likes to suppose that a designer intervened at each step, but they have already lost the war.
Simply put, there's no reason in generic ID why the designer would, out of billions (or a googol) of possible lines of descent, happen to build life in the one way necessary for NDE.
Of course, ID could theoretically improve its position. If ID can refine its theory so as to explain why the designer chose common descent, then it could narrow the odds.
The analogy in the card experiment would go like this. Suppose I change my theory about the random deck to one that proposes that the non-sorted deck was produced by a person who loved twos. Every one of the 52 cards is a two. In that case, turning over the two of clubs no longer gives us 98% confidence that we're looking at the sorted deck. Rather, we now think that there's only an 80% chance that we're looking at the sorted deck.
However, in creating a competitive theory, I have been forced to make a detailed prediction. This is where ID falls on its face like the fraud that it is. ID advocates generally refuse to make substantive predictions, and if they do make predictions, they don't follow from premises. It's not that ID is inherently unscientific, but rather that ID as it is today refuses to state a theory and place positive bets on the outcomes of experiments. In particular, until ID explains why common descent is observed, they're already at at least a billion to one probability disadvantage over NDE.