Does the EU charge other Non-EU European nations a comparable fee?
There were talks about such fee for all people from outside the passport-free zone, but AFAIK nothing concrete has been done yet about it, up until now, so should such plans get real after Brexit, it would look a lot like retaliation. Also, as the excuse for it is security, regular travelers having to pay it and clandestine immigrants entering without paying it would be quite ridiculous.
What are you talking about mate. Check your facts before misinforming others. Of course there is such a fee.
If you come from a non-EU country into a Schengen regulated country (most EU and wider, except UK), then you have to pay 60 euros to transit (ie, only pass through but not stay in the EU) and to stay for up to 90 days. Students, academics, and NGO workers are exempt as long as they are travelling on professional or academic grounds. If you come from a country that does not require a visa, then the fee, described as "pre-clearence fee" is set at 5 euros.