The problem is that a main condition of both a tourist visa and the visa waiver program is your fiance’s sworn promise that they only plan to visit the U.S., not immigrate here. The Department of State (“DOS”) and United States Citizenship and Immigration Services (“USCIS”) assume that intent to marry a U.S. citizen is the same as intent to immigrate. If your fiance enters the U.S. as a tourist, without disclosing that they are your fiance and intend to marry you, they have committed visa fraud. If the USCIS later decides that this is the case, they could be removed (i.e., deported) and it will be almost impossible for them to come back, even though they are married to you.
In theory, it is possible for someone to obtain a tourist visa for the express purpose of coming to the U.S. to marry. The problem is, to do this safely, they must disclose their intention when they apply for their tourist visa, and convince the consular interviewer that they truly intend to return to their home country after your marriage. For obvious reasons, this can be difficult to do, because the Consulates know that the K-1 fiance visa is available as an alternative. Even if the tourist visa is given, there is also a possibility that your fiance could be “turned back at the border” when they try to enter into the U.S. if the inspecting officer does not believe your fiance really intends to return home after your wedding. Finally, if you use this option, your fiance will have to return home after your wedding, and you will need to apply for a K-3 spouse visa or other appropriate immigration visa for them to be able to return to the U.S. a process that is just as complicated and lengthy as obtaining a K1 fiance visa in the first place.
Using the K1 fiance visa avoids all of the problems noted above, and is the only appropriate way for a foreign fiance to come to the U.S. to marry.