they are cable-less, thus need to be charged separately

Not a major drawback, IMO.

they are cable-less, thus it is easier to lose them

True, but I haven't lost any in the something like 6 years I've been using them.

bluetooth implementation is a potential security vulnerability

What's your threat model? Who's going to be attacking your security via your headphones? What happens if they succeed?

IMO this is a pretty ridiculous drawback, it's like saying "wired headphones are worse because the wire can be used as a garrote", which is true, but not an actual drawback for 99.999% of people.

transmission by radio will always be less energy efficient than transmission by wire

So what?

IMO the drawbacks of wired headphones are:

• The cable often gets tangled, and it's a pain in the ass to untangle it
• The cable can often get snagged on things, and if that happens the best thing that can happen is that the headphones can go flying out of your ears. The worst thing that can happen is that the phone goes flying out of your pocket and smashes on the ground.
• The cables can get dirty and frayed, and if they get too frayed they can break or get worn down so they have an iffy connection.
• Even when the cable isn't tangled, just arranging the wire so it's out of the way, long enough to get to your ears, but not so long it gets tangled can be frustrating.
• Trying to use your phone for anything else while your headphones are attached can be a problem. Say you want to take a picture of something, or pay for something using NFC, you have to be careful of the cable. If you had the cable tucked into your shirt or zipped up in your jacket so it's out of the way, now the cable might not be long enough anymore.
• Because of the wire, you're limited in where you can put your phone, and your head has to always be within a short distance to your phone. With a wireless headset you can choose to put the phone in a knapsack if that's more convenient, and when you put down the knapsack you can take a few steps away from it without losing your connection and interrupting whatever you're listening to.
• If you're doing something like working in the kitchen while listening to music or a podcast, you can't put your phone down on the counter and use it to look at a recipe, because as soon as you have to move to go get another ingredient, or to move from the cutting board to the sink, you have to pick the phone up again. And that can be a real issue if you have goop on your hands and you're moving to the sink to wash them off.
• In cold weather / winter you might want to have your phone in a jacket or something. If you go inside and take the jacket off you either have to pause things while you transfer the phone to another pocket and rearrange the wire, or you have to do this complicated dance where you clear the wire and move the phone without accidentally yanking the wire out of the phone or out of your ears. With a wireless headset you just take the phone and move it to a new pocket whenever that's convenient.
• ~~The headphone wire is a potential personal security vulnerability as a ninja can use it to garrote you.~~

The drawbacks for a wireless headset are:

• They tend to have batteries that can't be replaced, so eventually they lose their ability to hold a charge and need to be replaced. It can get really annoying to use them when the batteries are starting to fail and they hold less than an hour of charge.
• They tend to be much more expensive than wired headphones.
• Wireless buds are easier to lose, and easier to drop. If you drop them they can bounce and roll under things, or into the street or who knows where.
• They do eventually run out of charge, and you do have to charge them, and sometimes they can be low on charge / out of charge when you want to use them.
• There's a fair amount of lag, which can be annoying when you're trying to skip commercials on podcasts and so-on.