At least I found myself falling into that the last time I was between jobs -- constantly watching beginner videos on new thing X, Y, Z instead of actually doing something useful in one of them.
Back in employed world of course it can be the opposite -- you become a master of whatever tech your company is using but get little exposure outside that. It is however often possible to guide the company into a new technology and get the best of both worlds.
Training should be seen as a part of compensation. While there's some alignment with the employers needs, giving employees a training budget shoulder be seen as a cheap way to provide more compensation and they should be able to use it to hone their skills in whatever area they want, regardless of its utility to employers.
1. This differs more from workplace to workplace than industry to industry. Many dev workplaces will give developers a week or two of official "training time." Many other industries have workplaces that don't do that.
2. The reality is, training on new technologies has more value to you than it does to your employer. If your employer uses J2EE, Subversion, and Oracle, there's little benefit to them sending you off to learn Node, git, and Mongo. But there's a big benefit to you in knowing that, potentially. If the benefits of learning flow more to you than to your employer, you shouldn't be surprised if the burden of learning falls onto you.
3. But mostly, if you're a person who finds software development genuinely interesting (the hobbyist-type), you'll keep up on stuff basically recreationally. When you read about the latest whatever, you'll be curious and want to try it out and learn how it works because you're interested in that. You don't need any formal training to learn new technologies, just a little motivation and time. An hour spent not watching TV can get you a long way in understanding a new technology.