I missed the part where medkits count as kits, thanks for pointing that out. By that logic, from a RAW perspective all you need is a medkit (of any rating) to perform First Aid, as this would be a Biotech test.
RAW aside, I agree that it is somewhat unusual that First Aid can potentially be done with a 250 nuyen kit when toolkits used with other skills are 500 nuyen, However, I think the intent behind this rule could be taking into account the likelihood that someone who uses First Aid will also likely be using Medkit healing, and as such they will need to continue buying supplies.
Since Medkits can store 5 additional batches of supplies, one could argue that the more likely cost of a "first aid kit" is somewhere in the range of 250 to 750 nuyen, and unlike kits used for other tests Medkits will continue costing money over time. Until parts are introduced, no such extra cost exists for using kits with other skills; personally, I think that's a fair balancing mechanism.
EDIT:
Actually, a Lockpick Set is also 250 nuyen and applies to a specific situation (Engineering + Agility to defeat a mechanical lock), so I think a Rating 1 Medkit to perform a very specific action (Biotech + Logic to apply First Aid healing) is perfectly fine.