None of this explains how you explore a world you built.
In a D&D game that was eventually abandoned, the DM asked us each player to create a concept of one of the demon lords for this homebrew setting. Only name and concept.
I've already mentioned that due to the PCs staying some months between adventures in Baldur's Gate I let them, between sessions, create 5 NPCs with which their PCs had good, negative or neutral relationships (up to them).
It is extremely easy to implement, and some players actually rise to the opportunity, some don't.
There are other things my players have created within the game through character proses on our Obsidian Portal site.
Sure, as DM I can have final say, and I do, as I lean traditional in my approach but it is not difficult to let players derive a name for a rowdy tavern they frequent, a description of a clergyman with whom they have heated theological discussions with, a street urchin they financially support or a stray dog they've adopted.
There is a vast swathe of style of play between say a game by Lanefan and game by Pemerton. And to be clear, I'm not picking on these two posters, I'd probably enjoy a game by either of them.
The most important question at the end of the day will be, will YOUR table enjoy having a little creative input besides their input on their characters. I personally don't mind sharing some of the creative input even if I do not do it a lot.
The last time I allowed a PC to have creative input was on a magical item. I did not like the item within the DMG as I felt the mechanics did not fit thematically (player agreed) and so I changed it up offering two possible options for the item and each was mechanically different. I let the player select what they would prefer - interestingly they selected the more traditional concept.