They mention symmetries and invariances and what not but I wonder if it would be better to clearly emphasize that, in some problems, when you remove certain kin

They mention symmetries and invariances and what not but I wonder if it would be better to clearly emphasize that, in some problems, when you remove certain kinds of symmetries you are are combinatorially worse off. And this is ridiculously bad in some settings. Learning symmetries automatically used to be something I would see people working on but haven't kept up lately.