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Knuths definition of , is mskipthinmuskip.

LaTeX changes this definition to

DeclareRobustCommand,%
 relaxifmmodemskipthinmuskipelsethinspacefi

defthinspacekern .16667em 

amsmath.sty says it's

DeclareRobustCommandtmspace[3]%
 ifmmodemskip#1#2elsekern#1#3firelax
renewcommand,tmspace+thinmuskip.1667em

I might understand LaTeX's point to make a command usable also in text mode. But what's the point of the redefinition by amsmath?

You should look at the full picture:

 152 │ ifxleavevmode@ifvmode@undefined
 153 │ DeclareRobustCommandtmspace[3]%
 154 │ ifmmodemskip#1#2elsekern#1#3firelax
 155 │ else
 156 │ DeclareRobustCommandtmspace[3]%
 157 │ ifmmodemskip#1#2elseleavevmode@ifvmodekern#1#3firelax
 158 │ fi
 159 │ renewcommand,tmspace+thinmuskip.1667em
 160 │ letthinspace,
 161 │ renewcommand!tmspace-thinmuskip.1667em
 162 │ letnegthinspace!
 163 │ renewcommand:tmspace+medmuskip.2222em
 164 │ letmedspace:
 165 │ newcommandnegmedspacetmspace-medmuskip.2222em
 166 │ renewcommand;tmspace+thickmuskip.2777em
 167 │ letthickspace;
 168 │ newcommandnegthickspacetmspace-thickmuskip.2777em

The two definitions of tmspace are due to recent decisions to make such commands start paragraph mode anyway. With a recent LaTeX kernel the second one will be used.

Contrast this with the code in the LaTeX kernel:

1619 │ DeclareRobustCommand,%
1620 │ relaxifmmodemskipthinmuskipelsethinspacefi
1621 │ 

1630 │ defthinspaceleavevmode@ifvmodekern .16667em 
1631 │ defnegthinspaceleavevmode@ifvmodekern-.16667em 

4543 │ def>mskipmedmuskip
4544 │ def;mskipthickmuskip
4545 │ def!mskip-thinmuskip

4547 │ let:=>

The approach of amsmath is much more rational and cleaner. They also provide text mode equivalent of all macros, whereas ! cannot be used in text mode if amsmath is not loaded, and similarly for the others. The final result will be essentially the same. However, a , command will be translated into tmspace+thinmuskip.1667em when written in an auxiliary file, instead of ,. Not really a big deal.