What do Page and Peasant give you? Both give you the +action to build engines, both contribute economy, and both provide mild attacks. What is different?
Peasant's attack is more reliable, albeit often weaker, and peasant's economy is much more action based (Disciple quickly ramps up even weak action-cash; soldier can reach crazy heights but needs a lot of draw/action to support it, Teacher needs a lot of duplicate cards).
Page's payload comes from treasures. This makes page a lot weaker for making engine - you only want so many silvers/gold. Page can give you Labs, but almost always you bag at least one silver and that takes two turns to get there.
This drastically changes when each is skippable.
Easily to stock up on action cards? That just makes Peasant stronger - you can pick better cards to Disciple more easily, you can afford to start chaining Soldiers ($2, $5, $9) with surplus draw & actions, and of course that makes you Teacher tokens multiplicatively more powerful (hey I now have 13 buys). In contrast, Champion is the only Page line that really synergizes heavily with actions. And that is worthless if you can easily manage +action (e.g. CotR, Scheme, Lost Arts) this makes Page much more skippable.
No trashing/sifting? Page is much more skippable. Teacher can turn even lousy draw into good draw (e.g. Moat & Pawn can become Lab in the same game; which makes it easy to draw deck); Champion really needs terminal draw to matter and has trouble with adding more stop cards to the deck. Worse, when you do have expensive terminal draw you run into trouble massing it and not flipping the Page line. Getting a bunch of half-curses really slows down the Champion burn.
No +gains? Page is much more skippable. Peasant always can score bulk points if the game lasts long enough. Page needs something in the kingdom to fill out its potential (Remodel, +buy, Harem).
Killer attacks? Neither are really skippable.
Viable rush? Both may be skippable. Beggar/Gardens, Iw/Silk road, Rebuild, Hermit/Msqr, Donate fun (e.g. Fortress/Develop), and the like can win out before the the long term payout happens.
Lurker/HG might not be the best example there, because you can actually beat Lurker/HG by gaining a couple of Lurkers and using them to gain a bunch of free Hunting Groundses that your opponent is leaving in the trash and building an engine out of them, and the Travellers can help you do that.
Trashing 10 Hgs is game ending with 2 Estate buys. I have not done all the math but do you really have that many turns before the game ends? End game state is 11 green, 7 coppers and some number of Lurkers when you start triggering estates. Assuming I have just 6 Lurkers, I have > 1.25 lurker plays per turn. This empties Hg on T14 and you can certainly nab two estates in this time frame. Worse, if you buy Lurkers you remove the option of preventing end game by buy two Hgs to prevent on-trashing to estates as you can pile Lurkers quicker.
Champion is not going to make Hg safe to play until around T8 - T12. Even with village support, you have to play the shuffle triggering game wisely.
End point states for a Lurker rush are 35 vs 3 (0). So we are talking at scoring at least 26 points quickly. This puts you up to $21 payout. Certainly doable, but not on all boards. For a lot of boards you can expect one traveller to miss a shuffle ... this all seems to be very high variance.
Aku:
Pure terminal boards are not a death knell for Peasant, even without killer cards. Peasant itself is a non-terminal pile. Disciple on a new non-terminal makes for the ability to stack in new terminals; Teacher can then add other tokens to give you even more yields. Generally these are boards where you want something like every 3rd gain to be a Peasant so you can stack disciples. This works particularly well with good trashing like Steward (which also makes a nice Lab). Sure these boards are less Peasant friendly, but Peasant is just so flexible - he attacks, he sifts, he villages, he gains, and he increases payload.