I have dozens of wild thistles (most likely Silybum marianum, but there are several different kinds) in my yard.
Should I keep them, or get rid of them?
Their look is fine to me.
Would they aggressively spread? What would my neighbors say?
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I keep few of them, but if you are in an agricultural area and there is no abandoned place with a lot of them, then possibly some farmers will complain to you. Having happy neighbor farmer is a good think (they can help you with few things, maybe some fertilizer or manure or tools, and they could listen to you about how to handle boundaries zones).
For residential, I usually do no care: with regular maintenance, they should not give problems (maintenance and weed control is done more frequently). The problem arise when the plants are larger (and a lot prickly).
I like some of them. But from time to time you should remove them, so you can hate your choice (and possibly also your gloves will hate you).
Agricultural folk certainly don't like to have those in their lot, especially if they harvest the grass for their cattle. This makes bundles of straw totally unfriendly to handle once the thistles are dried out.
If some of your neighbours enjoy walking barefoot, it's the same, they will be unable to do it any more in their yard.
My advice is don't let them go to seed. Cut the flowers and put them under the composting pile to avoid the wind carrying them away.
I don't know what your neighbours will say, but yes, Thistles do spread quite readily. They also have a deep root system and are not that easy to dig out.
If you like the look of them, maybe keep some clustered together somewhere and dig out the others, but those windblown fluffy seeds will ensure you and your neighbours will forever be digging out thistles ongoing...