IIRC, Reinfeld's book groups the positions by theme. If you click the dice, it will show you a random position from the set, so that should give you a different theme most of the time.
Even doing it randomly, I found the content is extremely heavy on "play the most forcing move, ideally sacrificing the strongest piece possible with check". It took me 10+ problems to find one where this didn't apply (#659).
This would go down well on Reddit, where that style of puzzle is almost the only one appreciated. And it's a good way to quickly drill a few checkmate themes. But for chess improvement I would recommend a more general tactics trainer. IMO Chesstempo cracked the problem of automatically generating and rating interesting problems, but if you find the interface there too dated, lichess or chess.com have a reasonable second-best.
Is the goal to give players an engaging experience, or guide them through specific chess material?
I had a similar experience to the person above - after a few puzzles where the first move is the same I wasn't interest in doing more. I also don't want a random puzzle - generally puzzle progression goes from easy to hard - will random just give me a really hard one?
If you are set on keeping the order of _1001 Ways to Checkmate_, maybe giving some context on which chapter the user is on would be nice (Queen Sac, Forks). Otherwise as a user, if I don't want to do some unknown amount of queen sac puzzles over and over then I'm just going to bounce.
This would go down well on Reddit, where that style of puzzle is almost the only one appreciated. And it's a good way to quickly drill a few checkmate themes. But for chess improvement I would recommend a more general tactics trainer. IMO Chesstempo cracked the problem of automatically generating and rating interesting problems, but if you find the interface there too dated, lichess or chess.com have a reasonable second-best.