Cut them all down if you want a neater look, otherwise leave them. It all depends on how many you have to do!
If you aren't interested in the seeds that's the thing to do.

Connie

If it has seed pods, and you want to harvest seeds to grow seedlings, leave one scape with pods on it and trim the others off. If you don't want seeds, cut them off. They are not very pretty, and cutting them should send a chemical message to the plant to keep growing. (Well some hostas don't get the message, but cut them anyway for a neater landscape.)

Those are my two cents worth.

Lainey

Off with their heads!

"They are not very pretty, and cutting them should send a chemical message to the plant to keep growing. (Well some hostas don't get the message, but cut them anyway for a neater landscape.)"
hey_j

I don't have the research to say this but I believe once the signal to bloom is sent cutting bloom stalks doesn't change anything. The plant will continue the normal cyclical process.

Part of the process is which side of the solstice we are on and that varies by plant so saying a plant blooms pre-summer solstice or post-summer solstice doesn't matter.

For example; forcing plants out dormancy should only be done after the winter-solstice.