A will in Utah does not need to be notarized in order to be legal and enforceable. However, it does need to be signed by at least two witnesses, each of whom signed within a reasonable time after he or she witnessed either the signing of the testator's will or the acknowledgment of that signature by the testator.
Nonetheless, having your will notarized is a good idea. The reason for this is that a will that is signed by the testator and the witnesses in front of a notary public is considered a "self-proving" will. This means that the signatures on the will are deemed authenticate and witnesses will not be required to testify at subsequent probate proceedings.
This becomes very important in cases where one or both of the witnesses pass away or otherwise become unavailable before the testator dies. In that scenario, without notarized affidavits, it becomes more difficult to prove the authenticity of a will because there are no witnesses to testify to the authenticity of the signature.
Considering the relatively low cost and ease to get your will notarized, it makes a lot of sense to sign it in front of a notary public. Especially if it is likely that the witnesses will pass away before or around the same time as the testator or if it seems like the will may be contested.