I wouldn’t say handling wild animals is necessarily bad or unethical so much as it is unnecessary.
Generally speaking, handling most reptiles isn’t dangerous (at least, not for them!) but as @tiwane and @emjtca said, handling wild amphibians is usually not a good idea. Ask anyone who works in amphibian conservation and they’ll tell you just dangerous it can be! Amphibians have incredibly sensitive skin, and things that are harmless to us can be a matter of life and death for them.
Going back to reptiles, though, just because it’s not necessarily harmful to interact with a wild animal doesn’t always mean you should. If the animal needs to be handled to collect important data, or needs to be relocated for safety reasons, then I’m willing to give it a pass, but most of the time handling is unnecessary. Documenting an animal in it’s natural habitat is easier, less stressful for the animal, and can provide useful information on the habitat in question.
There’s an argument to be made that, especially with young children or people with phobias, it can be beneficial to allow handling, and I agree with that. In a controlled context, introducing people to often misunderstood animals can do a lot to reshape their opinions! But I also believe that we need to teach others, especially children, that observing for afar can be just as fun as getting up close and personal is. A lot of kids who love nature have a hard time seeing the danger it can pose, and how direct handling can negatively impact an animal. I was certainly guilty of this as a child, and though it never got me into any real trouble, it very easily could have. I’m still guilty of it, in some ways!
There’s something about being close to animals that most people find deeply appealing, and I can’t fault anyone for that. But if you’re going to risk handling an animal (and there is always some level of risk), you should do it for a good reason, and not just because it’s personally gratifying. If our love for nature somehow obstructs our ability to treat it with respect, then something’s gone awry.