I'd be very concerned about added color ending up gunking up the coil faster.
Metals don't get vaporised, and its really the presence of metals in eliquids I believe end up gunking up coils. And while I'm no expert on food colorings, metals tend to contribute to colours.
I am not aware of significant metals in e-liquids. In general even pure free-base nicotine has at most ppm levels, or less. Gunked coils is from thermal decomposition of flavors, PG, VG, nicotine, all with enough heat will decompose, and often into larger poorly vaporized compounds. Keeping the coil wet will minimize this.
I believe artificial colors should not be vaped, mainly because there is not much data on inhalation risks of artificial colors. Some people are extremely allergic to artificial colors. Some vendors do add colors to their juices, but I personally don't think that is a good idea at all. But it is not illegal. I think adding your own colors to DIY juices is risky, and does not benefit the taste at all. Many artificial colors are larger molecules that can decompose more easily than flavor compounds, VG, PG, or nic, and decomposition should always be minimized or eliminated. After all, it is thermal decomposition products of smoke that are so bad for you.
Colors evolve in some juices from nicotine oxidizing over time, and some flavor compounds can form interactions with nic-oxides that give other colors. Many vanilla juices over time will go pink. I do not think this is harmful at all, but then I do not think there is enough data on this to state that definitively. Seems very unlikely this is harmful, since nic-oxides are not, and the vast majority of flavor compounds are not.