These two things are related the other way round as well: to become a reserve currency, the using country must have a trade deficit. Else the rest of the world would not have enough liquidity to actually use the currency, and the market would grind to a halt. If no liquidity were available, any transaction would have to be secured with other assets. That asset would be the actual reserve currency then.

That's true, but it doesn't make it better in any way. Ideally reserve currency should not be the currency of any single country to avoid this situation where one country basically freeloads on the global economic development by printing paper and can even cause wave of global inflation by arbitrarily deciding to print waaay to much, too quickly.

You might argue that to keep printing this country needs to invest into aircraft carriers to keep everybody else in line and well behaved. But it's still a very profitable arrangement as the recent history of USA shows.