Hah! Yep, that seems true, the way it's phrased. Another example in which this is worse than Throne Room.
Same with Highway, you don't get any benefit of cost reduction. Doesn't reduce the cost of Peddler I think?
I think it'll really depend on the kingdom whether Procession is a good card or not. From the revealed cards, it looks like Procession will combo best with Squire, Fortress, and Ruins.
Squire: When you play Procession with a Squire, you get to choose between [+2 actions, +2 buys, gain a silver] TWICE, then you gain an
action attack card (thank you michaeljb), and then you also gain a $3 action card. Procession/Squire will be a great opening.
Fortress: This will be like playing a King's Court with a village, but with the added benefit of gaining a $5 action card. You play it twice, trash it, gain it back and play it a third time.
Ruins: Without a better trasher such as remake or chapel, Procession will play decently with ruins. Either you get a +$2, +2 buy, +2 actions, +2 cards, or the chance to discard or rearrange the top cards of the deck twice, and then you trash it goodbye. This all changes though if Poor House (or a yet unrevealed $1 action card) is in the kingdom.
Also, off the top of my head, Procession could pair nicely with Border Village if there is a good $5 card. Play the $5 card twice, trash it and gain a border village, and then gain back the $5 card. It'd be like playing a TR but you also gain a border village.