Paper dolls have been fun for a long time; the Lindy effect suggests that they will endure for a long time into the future.
The practice of playing with paper dolls has jumped from physical to software several times; KiSS and Palace dollz are notable examples.
Part of the charm of paper dolls is the combinatorial explosion. If the art is fun to look at and/or fantasize about, the combinatorial explosion means that fun is increased; I don't mean to imply that the fun is proportional to the number of combinations, that would be ridiculous. I'm merely claiming that there is some additional fun.
Below is a gif of a KiSS player and a Blockly interactable. You can drag a "doll" out of the toolbox into the area on the right, and then drag hair, tops, bottoms onto it, and it will snap together. This is a crude approximation of what using a KiSS player feels like.
Many RPG video games like Diablo II, Torchlight, or World of Warcraft also include a paper doll mechanic.
Below is a screenshot of Torchlight and a Blockly interactable. You can drag a "character" out of the toolbox into the area on the right, and then drag helmets, chest armor, and boots onto it, and it will snap together. This is a crude approximation of what the equipping and gemming minigame within Torchlight feels like.
Equipping your character, wearing and wielding particular items, might not initially be considered "the fun part" of Action-RPG games. However, game design is like humor. The non-expert listener perceives the humorous part of a joke to be located in the punchline, but the expert author knows that it's more accurate to say the humor is located in the setup. Similarly, the fun of hacking and slashing is partly powered by the potential for loot-drops, and the fun of loot-drops are partly powered by the fun of the equipping minigame.
During the equipping minigame, the player is thinking both about the equipment that they have newly received, and looking forward to the next session of hacking and slashing (as well as thinking about other things, like their fantasy of dressing in all black because they are roleplaying as an assassin.) Both thinking retrospectively and anticipating almost certainly makes the cognitive sensations of the hacking and slashing more interesting and/or more intense.
In each of these games, some equipment has sockets, which allow the player to choose which gems go into their equipment. This makes an instance of a paper-doll mechanic clearly translatable into a context-free grammar. Each type of slot, such as "weapon" or "gem" corresponds to a nonterminal in the grammar, and each particular item such as "Valcone's Gut Hider" corresponds to a production in the grammar.
character ::= CHARACTER LPAREN helmet COMMA chest COMMA boots RPAREN .
helmet ::= LEATHER_HELM .
helmet ::= DRAGONSCALE_HELMET LPAREN gem RPAREN .
chest ::= VALCONES_GUT_HIDER LPAREN gem RPAREN .
chest ::= BUCKLED_TUNIC_OF_THE_OWL .
boots ::= HEAVY_LEATHER_GREAVES .
boots ::= TALON_GREAVES .
gem ::= CRACKED_COLD_EMBER .
...
gem ::= THE_FIRE_QUEEN .
EVE Online has a paper-doll mechanic in a minigame called "fitting". Below is a screenshot of the fitting window in EVE, and another interactable. Again, you can drag a ship, such as an Executioner or a Condor, out of the toolbox, and drag high, mid, and low modules onto it, to get a rough feel for what the fitting minigame feels like.
It is important not to have rigid thinking that there needs to be an image of a person involved in order for the paper-doll mechanic to be in play. There is no image of a person in EVE's fitting minigame, and the different modules that one fits on a ship usually do not change its appearance. Nevertheless, EVE's fitting is a central part of EVE gameplay, supporting fantasizing about future possible adventures with your spaceships, and how effective they might be at various roles in various stories.
One final example, pushing the envelope of what counts as the paper-doll mechanic just a little further.
Unholy Heights is an apartment building simulator; among other activities, you furnish the apartments for your residents. You might imagine that some artist composited together furniture artwork in order to create an image of the apartment. However, you never even get to see the apartments that you carefully furnished to the tastes of your residents! Nevertheless, this is an example of the paper-doll mechanic.
In conclusion, videogame mechanics usually have a function to support the game's fantasy. By "fantasy" I mean the theme or the free-floating imagination-game that could be played even without a computer. The paper-doll mechanic in particular supports a feeling of "paying-close-attention-to" which is often part of an activity "taking-care-of".
In Torchlight or other RPGs, equipping and gemming is paying-close-attention-to your magical equipment and/or your avatar. In EVE, it is paying-close-attention-to your spaceship. In Unholy Heights, it is paying-close-attention-to your apartments and how they fit the needs of your residents, and so it acts to support the activity of taking-care-of your residents.
If you want your game to include paying close attention to something and/or taking care of something, consider writing down a context-free grammar of that thing, and turning it into a paper-doll mechanic within your game.
If your game involves playing as an evil genius in a lair, then possibly the lair, or the schemes, of the evil genius are sufficiently important to game that you want to develop a grammar of lairs (or a grammar of evil schemes) and allow the player to spend some significant fraction of their playtime looking at lairs (and/or looking at evil schemes) deciding which particular features their evil genius wants.
P.S. If you want to prototype your paper-doll grammar, you might consider using Tracery.