Is this really necessary, and are there any downsides to doing it?
If burrowing rodents are common in your area, then it’s definitely worth the effort. However, if they’re not an issue where you live, then it’s probably not necessary.
I don’t use mesh at the bottom of my beds because we don’t have burrowing rodents here. But if we did, and I skipped this step, I’d definitely regret it later when I’d have to dig out all the soil to install the mesh after the fact.
I definitely have moles, mice, and other burrowing critters, so I’ll stick with it and keep going.
You won’t regret it. It’s definitely worth the extra effort. Great job! 
“If there’s any doubt, then there is no doubt. The gut don’t never lie.” - Sturgill Simpson
I didn’t expect to see a Sturgill reference here!
Motor oil is motor oil; just make sure to keep your engine clean.
If you have mice, you’ll need 1/4 inch mesh. They can easily get through 1/2 inch mesh.
As someone with loads of voles in my yard, trust me, you’ll see the payoff come growing season. You’ll notice all the little holes and burrowing mounds around the outside of your beds from the critters trying to get in.
My chickens take care of the mice and moles, but if you have fisher cats, badgers, raccoons, or even neighbor dogs, any extra protection is definitely worth it.
I have the same issue. My beds with wire perform much better than those without. It’s impossible to start seedlings without the wire.
That’s why I didn’t bother installing a pterodactyl net over my garden!
There are many garden pests, and it’s impossible to tackle every single one. However, you can minimize the hassle by taking a few extra precautions.
Plus, not every area has rabbits to worry about.