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Perhaps, I may not completely understand the purpose of the ketubah in terms of it being a halachic legal document or a "shtar*. Aren't all legal documents supposed to be signed by the person drafting or responsible for its rules?

My understanding - if I draft a promisory note to pay someone a certain amount by a certain time, I gather that I would have to sign it, right?

The ketubah has many details on what the groom is obligated to compensate the bride. Shouldn't he be required to sign it?

The kesuba serves as documentary testimony that the groom accepted upon himself the responsibilities entailed therein. It is not an I.O.U., but it is the documentation of his acceptance. Consider the following text within the kesuba (this is taken from the RCA's version):

ב ______ בשבת ______ לחדש ______ שנת חמשת אלפים ושבע מאות ______ לבריאת העולם למנין שאנו מנין כאן ______ איך החתן ______ בר ______ אמר לא להדא ______ בת ______ הוי לי לאנתו כדת משה וישראל ואנא אפלח ואוקיר ואיזון ואפרנס יתיכי ליכי כהלכות גוברין יהודאין דפלחין ומוקרין וזנין ומפרנסין לנשיהון

(Translation of relevant line) The groom ______ said to _______ "Be my wife ... and I will support, and honor, and nourish, and sustain you according to the rules of Jewish husbands that support, honor, nourish, and sustain their wives..."

The document is testimony that he said these things (or, more pedantically in our weddings, accepted to have it written that he had said these things) in the presence of witnesses. The witnesses then sign it, and it is the authority of the witness testimony which creates the authority of the document.

Certain communities have the Chatan Sign the Ketubah. This was the custom in Egypt. Source to come later.

I am not a Rabbi, nor a halakhic expert on this matter. But this is what would make sense to me:

We are less interested in a signature of the Hatan, because it isn't hard for someone to say "that's not my signature." But rather the power of the ketubah lies in the witnesses who saw the Chatan agree to the terms. You would bring these witnesses to the beit din, rather than bringing the ketubah with comparisons of your husband's signature. However, I see no reason why a chatan couldn't sign a ketubah, and this is probably how it was able to be done in places such as Egypt.