Good analysis in the opening post and from @SavageJack pointing out that the dude retains their traits (helps Barton Everest, Tommy Harden etc) and goods retain their keywords (so they still work for Calling the Cavalry/Hex Slingin').
I agree that this is a very strong card that would encourage you to play Tens or to allocate some of your "off value" slots to this card if you aren't running Tens.
That said, I think your original post hits on one of the great balancing mechanisms of Doomtown, as the deck construction requirements mean this card isn't omnipresent.
Indeed, even in tournament decks where I'm running Unprepared I generally go 3x Unprepared and 1x Recruitment Drive as the latter is a huge help against slide/Spirit Fortress. There's the odd game where missing the 4th Unprepared hurts, but overall testing (and hopefully tournament results!) have shown that this is a reasonable policy.
If I 'm making a three value shooting deck with a few cards off value I often use cheatin' punishment cards as my off value cards (as I want to keep these in my hand and out of my Draw structure), so I often have one value with a job/forced callout (for example, 7 for Kidnappin/Run 'Em Down) or 8 for Bounty Hunter), a second value with forced attrition/hand rank manipulation (J for Hex Slingin'/Outgunned or K for Point Blank) and will then use a third value for my Shootout actions. Here I often find myself choosing between 3 for Sun in Yer Eyes and 10 for Unprepared, and a number of my tournament decks use 3s instead of 10s (https://dtdb.co/en/decklists/find?sort=date&gang=&lastpack=&author=harlath&title=) but have still managed to work.
The crucial reason for sometimes (but not always!) preferring Sun in Yer Eyes is making a dude a draw, as in an early shootout your opponent may only have one stud, or perhaps two at most but with the second only having one/zero bullets. That means with Sun in Yer Eyes your opponent with be X draw on a 5 or 6 card hand, while with Unprepared they'll be X draw on a 7 card hand and have a fair easier time making strong/legal hand. One extra stud makes a huge difference to probabilities with three value decks (a fairly common draw structure). For example, with a Law Dogs starting posse featuring Hattie DeLorre and a copy of Sun In Yer Eyes, even a posse with two 2-stud dudes can be dropped to a six card X draw shootout hand, while unprepared leaves your opponent with 7 cards X draw rather than their default 8 stud X draw.
Interestingly, several of the skills can now play around Unprepared (appreciate this doesn't help non-skilled decks):
- Hexes - Shadow Walk in and use an an attachment (Soul Blast, for example) before your opponent acts.
- Gadgets - can cancel Unprepared with A Slight Modification, and you can play as many copies of that as your opponent has copies of unprepared (albeit at the small cost of booting a gadget).
- Spirits - Totems get around Unprepared as they aren't attached to Dudes.
- Miracles - the one skilled suite that doesn't have a direct answer.
The above all said, Unprepared is very strong. I wonder if this would still have been playable if the ability had effectively been split over two cards, one that hits attachments and the other that boots a dude and gives -1 bullets. Not sure if it would have needed a "One Good Turn..." style "Noon: draw a card" ability to stop in being too narrow in some matches if it was split up like this?
I'm not from the rules team, so feel free to go to them for a formal answer as this has been covered before, but Unprepared dudes can indeed use abilities on Totems/Kung Fu cards. See below for the most up to date text on Unprepared, with my emphasis in bold. hope this helps. 
"Shootout: Choose a dude. Boot that dude and their attached cards. That dude gets –1 bullets and cannot use their abilities. Their attached cards lose all traits, abilities, and bullet bonuses. "
