That's not how it's described in any incarnations of Star Trek, however. And clearly the starships are capable of handling that sh*t-ton of energy.If the Transporter actually did convert every molecule of your body into energy (which would be a sh*t-ton of energy by the way) then transportees wouldn't be able to move their feet, talk, or grab lost space aliens - yet they do, in numerous different episodes and movies.
Clearly the Transporters operate in a different way than that which is just as well, since otherwise the Transporter would be an absurdly godlike piece of technology, able to duplicate Soonien androids and resurrect the dead with the mere push of a button - all you would need is a saved pattern and the equivalent amount of mass on the pad, ready for atomic rearrangement.
More likely, the Transporter operates by something like phasing its passengers (intact) into a nearby energy realm and then retrieving them at the destination point. This way, casual phrases like "converts you into energy" still hold up as generalised descriptions for the lamen, and a lot of the otherwise associated silliness is avoided.
Let's face it. the "science" behind fictional trek technology is dubious at best. I can accept the premise at face value, despite the inconsistencies of it's portrayal, since it's just a tv show. I enjoy trying to figure out what might make more sense or be more realistic but you seem to be taking that a bit further.