Is it always the case that when a reaction's products are higher in energy than its reactant, then the reaction is not favored?
This question brings up the broader point of what it means for a reaction to be favored. Your question describes thermodynamic favorability and that is just dependent on the relative energy of the products and the reactants. An analogy to this is to think of energy levels as literal heights subjected to gravity. If you have a ball on the ground (reactants) and you want to put it on a shelf (products), you have to put in energy. But, once it is in the product state, gravity will want to drive the ball back to the reactant state because it is lower in energy.

Another type of favorability is kinetic favorability; this relates to the rate at which the forward and reverse reactions can occur. There are cases where a thermodynamically favorable reaction doesn't occur (or rather occurs at an incredibly slow rate) due it being kinetically unfavorable. An example of this is diamond and graphite; it would be thermodynamically favorable for diamond to convert to graphite, however the reaction to do so is so kinetically unfavorable that you are unlikely to see it occur.