Now I suppose it would be possible to create outposts/installations that only have small landing pads, thus limiting what ships could be brought to those locations to initiate or complete a mission, but this wouldn't stop someone from taking a "smallcraft" mission, then switching ships at another station to an Anaconda, completing the mission, then returning to turn it in with a small craft.
True, but I'm not sure it matters. You'd still have to complete the mission in the small craft. If you wanted to ensure a particular ship was used, you could make it require a specific paintjob which the user probably wouldn't have and would probably not wish to purchase (especially if it was a limited-offer paintjob).
Small landing pads are not necessarily required for these kinds of missions. Here's an example:
Our agent has been <captured/killed> and we need for you to complete his mission in <system>. Our contact <NPC_name> is expecting to meet up with a <chrome/red/yellow/blue/etc.> <sidewinder/eagle/cobra>, so you'll need fly the ship we provide. Once you've met the contact and delivered the data-packet, return here to claim your reward and get your ship back. Enemy agents will attempt to disrupt your mission. Destruction of our ship will result in mission failure and a fine of <number> credits.
If the mission fails, you spawn back in the mission station in your original ship. Outfitting would not be allowed on a mission-specific ship. This could really increase the challenge level. I would assume you would have to be friendly or allied with the mission faction. I would think this sort of mission would have a large reward. Perhaps the reward would be the ship and its unique paintjob, which would only be available by completing one of these missions.
The current mission code probably can't handle something like this, but it would be fun to have these sorts of missions.