Can system:index be changed in an ImageCollection using map?

Question

I'm trying to simplify the system:index property of an ImageCollection containing Landsat 5, 7, and 8, images. Because collections are merged, they get 1_, prefixes in system:index. I'm sure that system:index is unique, so I'm trying to remove the prefixes using the following code:
Collection = Collection.map(function(image){return image.set("system:index",image.getString('system:index').replace('(d_){1,2}L','L'))})

but it doesn't seem to do anything. I understand that system:index, must be unique, and it is. Regardless, I would expect an error, if it's not unique, and not, not being allowed to modify it.
If I try to set a different property, in the same way, it works as expected, so the problem seems to be setting "system:index". Is it completely forbidden to modify "system:index"? Why doesn't it yield an error then? I couldn't find anything in the documentation about system:index being read-only.
// Works as expected, i.e. the SATELLITE property is changed correctly
Collection = Collection.map(function(image){return image.set("SATELLITE",image.getString('system:index').replace('(d_){1,2}L','L'))})

Link with testing code

Noel Gorelick · Accepted Answer

You can't change system:index with a mapped function, but you can set system:id which might meet your needs. It's used in preference to system:index in some situations (like when printing in the console).
If that doesn't do what you want, then you'll need to convert the collection to a list, map over that to set system:index (which doesn't have any special meaning in the context of a list), and then convert back to an ImageCollection.

Can system:index be changed in an ImageCollection using map?

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