iirc (but do not hold me to it) the plan was to allow exactly that however at the last min for what ever reason they had to drip it - presumably the sidey did not quite fit in the bay and bear in mind back in the day these ships were built with an assumption of interiors and being able to wander round in them so FD would not have been able to risk fudging it as we do not fly in a TARDIS
at launch in the description of the anaconda it was mentioned that it could carry a sidewinder. It has the bay door at the bottom that looks like hangar doors too.
I still have my sidewinder (0 credits rebuy with original parts, but fully engineered). I use it for memorials. It is also fun to fly in combat, unfortunately the Eagle MK II is slightly more fun, so that's what i use (allthough I do use a Cobra MK 5 atm, same reason, fun to fly).