Truth is, scanning consumes CPU cycles, which in turn consumes battery juice...
Also, if there's nothing to worry about, what are these AV apps doing? Scanning with an empty database?
That's why it should be avoided at all costs and ignore the so-called anti-virus products as that's fear-mongering into scaring you psychologically and likely, end up "paying for their product" so that you'd feel 'safer' and lulling you into a false sense of security!
Ultimately it boils down to a bit of common-sense and double-check on the reviews and weigh it up carefully, users are not likely to bother reading what sort of permissions there are, the reviews, and so on, especially, from countries where buying an app is impossible due to legalities and restrictions within that country's jurisdiction and laws!
In relation to permissions, that is why developers post explicitly on the Overview page on the Play Store, what sort of permissions there are and explain it, around the top of the page, due to the fact end-users themselves are not bothering to click on the 'Permissions' tab page!
Henceforth, for some users, who do not want to buy, they ultimately end up being the victim and also for users from these countries, which end up resorting to downloading from unknown and dodgy websites, so don't be downloading from dodgy warez websites either!
Pro-tip If you happen to be in one of those countries or that you don't want to buy, email the developer of the app personally and ask them if some sort of agreement can be made, it can be done, perhaps by using paypal or similar... developers are not "out to get you", in fact, they are friendly! :)
YES to be blunt, Android apps can easily, be modified by someone who has knowledge of the code, due to their nature, and quite likely, to have some malicious code (read not virus.. but a trojan!) that fools the user, into thinking the app is "all-good" when in fact behind the scenes, it is sending out some logs/emails etc... that is often the reason why there should be a firewall in place to block unknown apps for a few days and monitor it. The sad truth, is, no-one gives a damn or care about that and end up posting "why is my phone bill so high?" or "Why is my battery getting sucked down very quickly?"
It is those clues that are the dead-giveaway of something quirky going on and should set off alarm bells in the head as in "Oh, that's funny, ever since I installed X app, this started appearing" but are the end-users going to care.. and carry on in denial...?
That is where the so called Anti-virus software vendors kick in... hence a vicious circle ensues...
Not to be an alarmist, remember this much: Android is not equal to Windows where viruses and malware are more commonly seen and prevalent!