The Scroll of Secrets is worse than the one, that's for sure. But Mystics probably haven't access to that, so let's make a few points on Scroll of Secrets in a pure after playing it. Yes, most things will work with the counterpart. I'll speak exclusively about the Tabooed versions (with the ability).

• If you go Down the Rabbit Hole (maybe you primary upgrade your spells just with Arcane Research) this costs you 2 XP, which feels like the right spot experience-wise.
• 4 Secrets for 1 Resource is very solid, especially if you want to spread secrets with Eldritch Sophist across the table. Only Encyclopedia (2), Schoffner's Catalogue and the upgraded Ancient Stones may offer the same ratio, while Forbidden Tome (0) and Forbidden Knowledge are slightly above.
• If you use all the secrets for draw (not discarding, not leaving them there and not for manipulating the encounter deck) overall you get 4 extra cards in windows (one more card than the Scroll, though you can't pick one of three).
• There is a bit more competition for hand slots these days, but in general Mystics have hand slots to spare, unlike Seekers.
• Gone empty, it's a great target for Dexter Drakes ability or for Sacrificing to get resources or even more cards. If you have access to level 1 cards obviously there is Library Docent, too, for repeating the fun.

As people mentioned, the most interesting difference to the Scroll is looking at the top card of your deck and being able to discard weaknesses you would have drawn next. With the one you can delay them (putting cards from the bottom on top), but probably you have no knowledge of weaknesses sleeping at the top of your deck.

The effect sounds like the old Alyssa Graham Trick protecting you from Doomed and stuff, but therefore you just put the card at the bottom of the deck (drawing it later) and have to add doom. Also if you're like me you could forget, that you shouldn't activate effects which reshuffles your deck...

That said, Mystics are the masters of “look at” and “return in any order”, so you have a chance to manipulate your deck in order to discard nasty weaknesses like Doomed, Offer You Cannot Refuse or Unbound Beast. In the past there wasn't much more than Scrying, but with the release of EotE we have Parallel Fates (2) to celebrate, which lets you look at 6 (!) cards. In mid-/lategame (or using Underworld Support for smaller deck size) there is a realistic chance to draw an important card with Parallel Fates (2) AND discard 1-2 weaknesses with the Scroll. And even without manipulating effects, I randomly hit a weakness or two with the Scroll and discarded them in my play-through (which may happen often in the Edge of the Earth campaign due to spoiler reasons).

The option to look at the bottom of the deck is neat too, if you've drawn Doomed and want to discard Accursed Fate or if you have Wendy's Amulet or a Copycat player at the table. Speaking of this, as with the other Scroll of Secrets it's a great multiplayer tool because you don't have to be at the same location in order to look at another investigators deck.

The best weapon in true solo, where you often need your other hand for a flahlight, keyring or magnifying glass. Also the bosses you meet at the end don't have as high health as in multiplayer. I usually play this with autodamaging allies, such as guard dogs, brother Xavier and beat cops to make the charges last. It is tempting even in solo to go for the big guns when purchasing new cards but I find they're usually overkill. This card though does it all: Leaves one hand free; kills the enemy; gives you cards and cash for the trouble so they can help you find the clues afterwards; and it helps your jumpy guardians keep their sanity.

Since the location gains the effect, then Lola Hayes can trigger the effect in any role, right?

Being Lola, this opens so many possibilities. And that without the drawback of needing to be in the role at the right time.

After playing for real, I found that the 3 charges effect (free action) is surprisingly hard to make use (similar feeling to having Leo De Luca but it is just quantity not quality) and make you want to reset the clock early (take just 1 or 2 resources) in order to go for that +3 skill value that looks more in immediate need. Which if you did at 2 resources, you wished that you had done so earlier when it was going from 1 to 2 charges. So, it has more depth than I thought. +3 skill value was a happy turn almost every time. (e.g. Bob Jenkins can reliably activate Scavenging here.)

An unexpectedly good use case for that 3 charges is if your party have got those lame weaknesses that requires to fix, which any investigator at the same location can help. They often stick around for long time, creating more right moments when the clock comes to 3 charges.

You should look at the clock and plan for a meet up with your friend, especially at 2 charges leading to the extra action when you can move twice (this is kinda fun on its own lol), and then spend actions to fix it "at discount". Other than this, there are also sticky treacheries on investigator and location that you can help fix with your extra action but if it is a test (mostly?) then Rogue may not able to help that much.

Awesome card for Mark Harrigan! Whenever i play solo with our famous soldier, i take this card. Basically, it gives you 2x Unexpected Courage from his ability and a card, which you can count like it replaces itself. Pretty good value if you ask me.

Most of the time the restriction of it being the first action won't really bother you, and you will almost always be glad to see it in your hand, knowing that you are free to take another quick peek at your beloved Sophie!