Can Asterisk be a softswitch between sip and h323 and mgcp?

It makes me bewildering.

You have to realize that Asterisk is totally biased towards SIP.
As it should be!

I read that there is some support for Open H.323 but just the compilation of the module is quite a challenge.

In other words, if you run into trouble with H.323 all the help you are going to get will be in the form of “You are on your own” and “I told you so”.

The reason they picked the word “Simple” in SIP was to contrast it to H.323 which is extremely obscure and hard, not for technical reason, but to place the standard outside the reach of “the rest of us”.