The downsides to a charger being "permanently on" is firstly that it uses electricity even if nothing is connected. But as the cost of that is a lot less than a penny a month its not a deal breaker.
Secondly, as its a transformer, it has a finite life cycle. Even switches that are rated for a million operations will likely fail before they get to 2 million, and transformers will also, eventually fail. But even so, although being on 24 hours a day, that charger should last several years. And if like this, its on an extension lead that gets switched off, only the very cheapest of units are likely to fail in your lifetime.