For new players who are just dipping their toes in Dominion waters, often just the Base set or maybe 1 expansion will (and should) be played.
This means that Woodcutter with its +Buy doesn't have that big of an impact, since most strategies will focus on buying a lot of money with just a few "terminal" actions. An action is terminal if it doesn't have +1(or more) Actions on it.
So Woodcutter is a terminal action and so is Militia. But Festival (+2 Actions) and Market (+1 Action) are not.
The earlier mentioned Gardens strategies are really strong if they can be accelerated with Woodcutters or Workshops.
So we come back to our choice of preferred terminal actions. If I open 4/3, I rather take a Militia/Silver than Militia/Woodcutter or Silver/Woodcutter. Militia is a lot better than Woodcutter in regular Province games. Some other good basic $4's include Smithy and Moneylender and even a Remodel can come in handy (especially in the end game for upgrading Gold to Provinces). A lot of these $4's are better than Woodcutter since the number of times you absolutely need that +Buy with just the base game are rare (see Gardens example above). If we find ourselves with $6 and two buys, buying one Gold is a better than 2 Silvers.
Quick math here: Let's assume we have $20 total coin output in our deck and 20 Cards. Buying 2 Silvers will increase it to $24/22 = an average of $1.090 per card. Buying 1 Gold will increase it to $23/21 = $1.095 per card. This difference goes up in favor of Gold as the number of total coin increases. Also it's worth mentioning that in Dominion, having one good turn and one bad is usually better than having 2 mediocre turns. That's why 1 Gold is better than the 2 Silvers. You'd rather be able to buy a Province and nothing than have to resort to buying 2 Duchies.
Coming back to the actual Woodcutter in question and our discussion of terminal actions: The Woodcutter would be a lot better than Silver if we are guaranteed to be able to play it every single time. Unfortunately, there may be a lot of other terminal actions which are also very good, think about a Witch for example, that we want to play. And now there is a chance (and a very big one) that at some points, we have to choose between playing the Witch or the Woodcutter, since we have only one valuable action. And we may draw the Woodcutter with the Witch and not be able to play it.
This means that, in practice, the Woodcutter does not give us $2 or 1 Buy every time. We can say for certain that it will give us that some of the time and if we twist that logic a bit, we can say that on average, the Woodcutter gives us <$2 and <1 Buy (for example $1.5 and 0.75Buy) every pass of our draw pile.
In conclusion: Remember that the Big Daddy cards (the cards you want more than one of) all cost $5+ and even with a +Buy, it's hard to be able to buy multiple of them in one turn. And then there's Festival which 1-Ups this card. If we find ourselves with $7 and 2 Buys, do we really want a Laboratory with a useless Moat? Or do we take a single Gold or even a single Laboratory instead? Good cards are expensive, so this leaves less money to spend with the extra Buy and another useless card is usually not something we want in our decks.