Great idea. I was really stupid and got rid of the most of the achievment items including the infamous Ghostly Gibus and HHH's axe not to mention those cool items from SMNC and PN2 and I'll gladly pay for this ticket if it's added. However, there are multiple problems with this idea that would make adding this item a pain.

Issues:

1. There's a catch. Most of the mentioned items are promotional which probably makes the legal side of getting them back finicky so if it's implemented it will probably allow to get only TF2's original achievement items back but honestly I'll take it over having no such option at all.

2. There would probably be difficulties of tracking the amount of items per account because this item, as described right now, would require the game to check the whole inventory for items from its pool so that it wouldn't pump out duplicates of already present items.

3. Changing achievement items' quality to Normal would screw over already existing items like HHH's Headtaker since being unusual (As well as not being... you know, the axe itself because the achievement's reward is the metal not the axe) is one of its unique traits not to mention that it would require going over every single inventory and changing already present achievement items to that category which would ALSO screw over achievement items with killstreak kits like Lugermorph, Big Kill, Iron Curtain, etc..

4. The amount of items it would restore would be highly inconsistent due to its dependancy on multiple different factors so it would also need a dynamic pricing/crafting system to scale the price depending on the amount of missing items that can be restored. Doubt TF2 team would go that far.

5. Adding one and done item generally doesn't sound like a good idea.

Proposed changes to raise the chances of TF2 team accepting this item:

1. Only restores OG TF2 achievement items

2. Gives out every achievement item in the game in their original form (i.e. Haunted Metal Scrap and not the Normal HHH Headtaker)

This eliminates possible legal problems, keeps killstreaks and qualities intact, allowing players to do whataver they want with their items besides things that weren't allowed to begin with and making this item more useful while eliminating the need for complex tracking systems.
Perhaps it could be more of an "Achiever's bundle" like those that are sold in Mann Co. Store idk