If you start practicing HT, everything you do, including the mistakes, stuttering, unnecessary movements and tension, etc., will be memorized by your hands and included in your playing. So unless you're a good sight-reader and can read across whole sections with HT and no stuttering you should do HS. The reason for working hands separate is simple: first figure out the fingerings, expression, dynamics and tempo (HT speed will always be slower than HS speed, so you want to achieve a faster speed than performance speed in each hand), and then work on coordination. If you try to do all that at the same time it's too much, and you'll most likely mess up, unless of course you're an expert. Also, most of the times one hand is more interesting and elaborated than the other, so you'd be training them unequally.
I used to practice hands together from the start, and even in pieces when the left hand is repetitive and pretty simple (like a Chopin Waltz or Nocturne Op. 9 No. 2), some notes wouldn't sound, the chords weren't clear enough, etc.
But in the end it's up to you, you could take 2 pieces or two sections of the same piece that are similar, and practice one HT and the other HS until you can play each hand faster than final speed, put them together and after sometime see how both methods go.