Charging for vowels is just one way in which the program gives a nod to the old Wheel Of Fortune game. Another is the fact that it offers WOF bonus puzzles (i.e., "Same Name", "Before & After", etc.) At the beginning of the first game, you have no points and so must guess at least one correct consonant before being able to afford a vowel. As games continue, vowels become more expensive. The idea is that clever players will use letter-frequency knowledge and context to guess the most likely consonants first (s, t, r), thereby saving themselves point expenditures. As your post suggests, you could take a different stance.
The problem I have with this is that you can't really save yourself any point expenditures because you must
pay for the vowels one way or another to solve the puzzle. If the game were like Wheel of Fortune where you could "solve the puzzle" without paying for more vowels or the risk of losing your turn from an unlucky wheel spin, then that would be a different story. But since you must enter all letters to complete the phrase, it doesn't matter whether you do vowels first or last, they must be entered (and paid for
So in practice all it really does is make the player guess a correct consonant or two at the very beginning of the first round and then the only purpose it serves is to progressively penalize players who are trying to compete on the leaderboards and just so happen to get phrases that have more vowels than other players.
In my opinion, charging for vowels only makes sense if you can win without using them.
Another couple of problems I have with the game that make it feel unfair:
The bonus puzzles or themes are not always clear. I've never really been that into Wheel of Fortune, so telling me the theme was "Before & After" wasn't very helpful. I was thinking it meant something like dirty and then clean, or fat and then skinny, or an apple (uneaten) and then a core (eaten). Fresh and then rotten. From the description of "Before & After" it isn't obvious that it was two separate "word associations" with a common word in the middle.
Since Hangman is generally a test in your ability to spell or your knowledge/understanding of words/language, it isn't fair to put quotes with author's names. Since people's names can be spelled all sorts of ways that don't follow the rules of the language, or could even be (or have roots in) a different language altogether, names seem to me an unfair difficulty.
But then again, maybe I'm just griping because normally I'm pretty good at hangman and this game is so unlike any version of hangman I've ever played before that I'm not very good at it.