An active transporter "costs" ATP. One way you might be clued in that active transport is necessary is if a protein channel is going against a gradient and there is no counter-gradient or symport mechanism to help it along.
Enzymes are catalysts- they simply lower the activation energy and let you get through a prohibitively unstable transition state more quickly. The transition state still forms, but due to whatever interactions with the enzyme, it's more stable that it would have been otherwise. Use of enzymes does not "cost" any ATP. They work because of induced fit, that is, once the enzyme bumps into the substrate, the most stable situation is when the substrate forms transient interactions with the exposed amino acid portions of the enzyme's active site.
The transporter is like an enzyme in the way that it also relies on those transient interactions to let it hold onto whatever it's trying to transport. So let's say you had a transporter protein with a mutation- instead of having, I don't know, methionine lining the channel, you instead have valine. If it's an ion transporter, can it still do its job in the same way?
No. Now it has hydrophobic residues in its channel, so it will be more difficult to carry charged ions. Same concept applies to enzymes- a mutation that makes the active site interactions with the substrate less favorable will lessen the efficacy of the enzyme.
As far as all transporters being enzymes.... I don't think this is the case, although I'm sure AAMC would be able to gleefully cough up a counterexample🙄
Enzymes catalyze both forward and backward reaction according to the product/reactant ratio dictated by Keq of the reaction. So actually enzymes DO bind a little bit of product and let it go back to reactant (according to TPRH, just read this.)
On the other hand, since most active transporters just "spit" ions without changing them, if you reverse the energetic environment, there's really no reason it couldn't just start spitting the other direction as long as the ions were still able to make it into the channel.
As far as I know, the thing that makes active transport "active" is its energy requirement. That means that it's nonspontaneous. The ending situation (say, pumping Na+ into an area where there's already lots of cations) is less stable than the beginning situation. So, you have to use energy to make it happen. This is different than just having a high activation energy but having and end situation that is more stable than the beginning. Such a reaction would still be spontaneous, because spontaneous vs. not is defined by comparing product stability to reactant stability. So in theory, I guess it would be passive if the circumstances were going to let the transport happen without input of energy.
