I think tool proficiency is a pre-requisite i.e. a requirement to be able to even have a chance in success. For example, you can't try and disarm a trap with thieves tools, unless you are proficient in thieves tools, however you disarm using a Dex (investigation) check. To play a lute, you need proficiency in the lute (or at least proficiency in stringed instruments, if you are more generous), then your actual playing uses Cha (performance). The DMG magical instruments support this, for example last night my group got magical pan pipes, which required proficiency in wind instruments to use (and it turned out one PC had actually taken proficiency in pan pipes).
Think of it like this: if you've never played guitar in your life, or anything similar, do you think your 'perform' skill is going to help you play the D&D equivalent of Stairway to Heaven?