I don't consider lacking +1 Action on the first play a "major nerf". But if it's an issue, there's a simple fix, albeit one that buffs Adventures cards: just change "face-up" to "face-down'.
And it's an even bigger nerf in a second way: if you 'power up' the Pilgrim by going with just the +1 Action, then you have to collect your benefit the next time you play a Pilgrim. You can't save the +1 Action, +3 card play for when you need it.
Sure, you have to collect the benefit immediately, but with the previous version, you have to pay the cost immediately instead. You can use Pilgrim in the middle of your turn, but if you don't have 2 more Pilgrims in hand your turn is essentially dead. With the flipped version, you can delay paying the cost until your deck is already drawn.
In general, it's better to play your strongest draw effects at the beginning of your turn, and your weakest draw effects at the end. This is why I suggested the change. And since +Actions last until the end of your turn, it's not an issue to take +Action at the start of your turn if you can spend it later on.