This is a matter of personal taste. I cut them off because I think the plant looks better as the bloom stalk declines. I cut them off down in the clump so they are not visible. I'm not crazy for the bloom on some hosta but others are attractive. I'll post a couple of pictures. I've haven't had any rebloom.
I agree that it's a matter of personal taste. I am not a hosta flower scape fan and usually spend some time every week cutting down the "spent" scapes. And some are much more "ugly" to me than others. My first hostas to lose their scapes around here are the ring of Blue Mammouth hostas that I have around one of my trees. When I see them start to emerge, I know their end is coming! Maybe it's because there are so many of them all together and they bloom at exactly the same time.
No harm to the plants. I do the same as Paul - cut them down below the tops of the folliage of the leaves so they don't show.
BUT...this year I have decided that the scapes of the minis are just too cute to cut down early. Time will tell if they get "ratty" looking to me. But for now, I think that the tiny little flowers look awesome.
I used to cut scapes after blooming. It is said that HVX doesn't transmit after blooming but I am not taking any chances. I no longer hop from plant to plant cutting anything. Now I just leave spent scapes until they can be pulled by hand once they have dried up. I have noticed more seedlings coming up here and there since I leave the scapes on. My Empress Wu has about 50-60 little seedlings going half way around it.
I want to thank everyone for their responses. Right now, most of the blooms are gone. I'll be out at 6 am cutting them back. Oh, and I didn't know I could collect seeds from them. Maybe I should ask how that's done and what to look for before I cut them back!!! Any takers?
I only know the name of one of my many hostas because I bought them and planted them myself. It's a Blue Hosta. I'm new to gardening these and that's all I know. The stalks on those are just now starting to grow.
However, all the other hostas are of the same variety (I have no clue what they are called) but the stalks are an average of 3 feet tall!
My only real concern about cutting them back (especially now that the blooms and gone) is that half of that 3 feet has leaves here and there on the stalks themselves and was afraid I'd be killing the Hosta.
You can collect the seeds, but be forewarned that hostas in general do not come true by seed. Expect of lot of nondescript green hostas. However, you MIGHT get a surprise. I have one seedling that early in the season is two colours though it greens up in July. I have another that is a lovely marginated plant - reverse colour of its parent. You might get some with red petioles or wavy leaves and only time will tell whether they are worth keeping.