I love how you're equating Discover Magazine with the tabloid reporting that the mainstream media does. They employ people like Phil Plait, so they actually know what they're talking about.
Ugh, I have read many popular science magazines, and many of them don't actually explain special relativity's Twins Paradox correctly. They always leave it off as one is older than the other, and that is a paradox.
It isn't. The paradox is the fact that in both of their point of views, they are the one stationary. Then why is one older than the other? The paradox is resolved by the fact that one is accelerated when returning.
I have never seen a popular science magazine properly describe this. You must read the journal paper itself, not just a simplified version of it (which may even be completely wrong) on a science magazine.
What's wrong with them using the same evidence as the old theory, if it works with both?
Because if the old one works just fine, there's no need to replace it with something else just because it is simpler.
The simplest explanation of a lot of things is can often be reduced to a variation of the anthropic principle. Take g for example.
The current theory is that g is determined by Mass of Earth over Radius of Earth squared times G.
A simpler theory is that, if g were any different, it would have affected our evolution, bone, and muscle structure. But since our bone and muscle structure are the way they are, we just happen to live in a world with g being 9.8 m/s^2. (the point is that it is not correlated mass, but rather it itself is a constant)
Sort of like every possibility exists, but we just happened to be living in a possibility that worked out this way.
Does that explain things better? No (nor worse. It just says that every body has its own value of g. It fits all of the data). Is it simpler? Yes.
Only if it works better do we replace it. If there is absolutely no distinguishing difference between the predictions of A and B, we adopt the one that was developed first as mainstream, and maybe mention the second one as an aside of a different interpretation. (see Many Worlds vs Copenhagen interpretation of QM. Copenhagen was developed first, that is why it is kept, rather than the many worlds which I myself favor on again, philosophical grounds, which mean nothing in the science realm)
Since the cyclic model
has distinguishing differences, we hold onto the old model which has withstood its own tests already, rather than adopt a new one which was fine tuned to fit the existing data, until appropriate data comes in to test it.
What if your new model is wrong? Do we go "Just Kidding! Go back to the old model while we think up of a new one to test." The only people who will benefit from this is the text book companies. We keep the old one until it is definitively defeated with a better model, not replace it with a simpler one that makes the same predictions, or has a more detailed prediction that has yet to be verified.
Using your logic, the geocentric theory of the solar system is the correct one. It was the established theory when the heliocentric model was proposed, and is only better because it's simpler, and as you said, simpler =/= better.
And yet somehow the heliocentric model overthrew the geocentric one, even in an era before space probes! Gee, I wonder how that happened.
No. Initially the Heliocentric model actually required epicycles just like the Geocentric model. They just presented it as an alternative to simplify the math. It didn't predict it better, it was just simpler, and they kept both ideas around, but primarily used Geocentrism. It was only after the model was refined a bit (confusing ellipses instead of circles, which are arguably more complicated), and made predictions that differed from the Geocentricism model, and it was verified did they change it up.
Geocentricism does not correctly explain things like phases of Venus (Galileo), the fact that moons orbit around other planets (Galileo), and that Gravity is observed to behave as GMm/R^2 in non-relativistic scales (Newton).
Heliocentrism explains it
better. It just happened to be simpler. It didn't replace it because it was
simpler, but rather
better.