Why is there no rule allowing a player to claim a draw in lonely king endgames? I was wondering, why is there no way for a player, who has sufficient mating material, to claim a draw against a lonely king?
According to Wikipedia:

The rules allow for several types of draws: stalemate, threefold or fivefold repetition of a position (with the same player to move), if there has been no capture or a pawn being moved in the last fifty or seventy-five moves, if checkmate is impossible, or if the players agree to a draw.

For example, KQvK is very obviously an endgame with only two results possible: White wins or draws. But according to the rules of chess, White cannot force his opponent to accept a draw on the spot. Offering a draw could be refused, and also giving a check on a square where Black could capture it could also be refused by Black by moving somewhere else.
Ok, let's be realistic for a second, 99.99% of the time this won't happen.
But somehow I find it counterintuitive not being able to end the game in this particular position without having to resign and entirely lose the game in a position where it's impossible for Black to win by checkmate. Especially since you've already proven that you're at least capable of making a draw against your opponent.
Of course, I'll admit such a ruling would be more of an edge case. But still, there's somehow a gaping hole in the rules of chess.
Why is there no rule allowing a player to claim a draw in lonely king
endgames?

For the simple reason that there is no need. If you are the player with the extra material you can offer a draw and be almost guaranteed that your opponent will accept the offer. If you have an opponent who is ignorant of the rules you can walk away and let your clock time expire and the game will be a draw.
This is what the FIDE Laws of Chess have to say:

6.9 Except where one of Articles 5.1.1, 5.1.2, 5.2.1, 5.2.2, 5.2.3 applies, if a player does not complete the prescribed number of moves in the allotted time, the game is lost by that player. However, the game is drawn if the position is such that the opponent cannot checkmate the player’s king by any possible series of legal moves.

A player with only a king cannot checkmate the opponent and so the game is a draw.
EDIT: Remellion makes an excellent point in the comments which is worth repeating -

Technically you don't need a new rule - under 7.5.5, you can just make two illegal moves in front of the arbiter, ending the game immediately (as a draw, similar to when your time runs out but cannot possibly be checkmated). No need to bloat the rules more

You don't even need to wait until the arbiter is watching your game. You can deliberately complete (by making the move and then pressing the clock) an illegal move, stop the clocks, explain to your opponent that you have made and illegal move and then call the arbiter to report yourself. While the arbiter is there explain to them that you are going to make a second illegal move to effectively claim a draw. That way you don't annoy the arbiter by calling them back twice.