I think its important that all maps as part of an episode should be designed with a Shotgun Start in mind as a standard, regardless what weapons the previous level offers - or at the very least keep those in mind and not worry too much about bumping up the challenge whatever players choose to do.
I always start from a clean slate once the next level boots up, it keeps thing interesting and should allows mappers to tailor gameplay to their level as they see fit for those who choose to take this approach.
Sadly these details could be missed out on but find it's preferable to have that option available. Reminds me of a Doom episode still fresh on my mind, "
Going Down", where some levels (ex MAP03, MAP15, MAP18, etc) can lose their unique flavour when carrying over weapons often reducing the tension or challenge.
... that's my 2 pence