I switched to e-cigarettes and I cough less, have a better sense of smell and taste, and I feel healthier, what's the problem?

Just because you feel better doesn't mean that you are "healthier". We don't know the long term effects from vaping yet. It certainly will NOT be the same as with traditional cigarettes but e-cigarettes will have their own disease profile. 

Part of the problem is with the flavors--while they may be GRAS for ingestion, most have not been tested for inhalation. 
e.g.  Lawsuit Filed Against Butter Flavoring Companies and Popcorn

https://www.femaflavor.org/safety-assessment-and-regulatory-authority-use-flavors-focus-e-cigarettes


What may be harmless when eaten, may be toxic when inhaled. Just as the tobacco leaf has about 600 chemicals in it but when lit turns into about 7000 chemicals, the few chemicals in an e-cig may turn into other chemicals when heated. We do know that the temperature influences how many chemicals are created int he vapor, which can be different for every user because everyone uses their devises differently. 

Not coughing can also be a problem since coughing is the body's way of clearing out the lungs. Smoking paralyzes the cilia of the lungs interfering with the lungs ability to clear out the components of smoke. Not clearing out the lungs can lead to more respiratory infections.

Just as other vices have their own risks and benefits, users need to weight those risks and benefits and make their own decision but until we have long term health information, the actual risks are unknown.