IIRC, the module explicitly notes that characters don't have to take part in all the missions. As a matter of fact, it's extremely difficult to do so. As I noted in this thread
here, the goal of module is provide many varied paths to leveling up by the encounter's end. If a party is very careful, rations its resources, and avoids fights as much as possible, and comes away with the minimum XP for all the missions, they end up with 399 XP. If the party gets into a lot of fights, they will blow their resources much earlier, but also earn enough XP to not need to complete all the missions.
Aside from the bookends of Seek the Keep and Half-Dragon Champion, there are two keep-based missions (Dragon Attack and Sally Port), two village-based missions (Save the Mill and Sanctuary), one that is in-between (The Old Tunnel), and a bonus mission that can be completed during any of the other missions (Prisoners). Each mission takes up an hour of game time. Except for the bookends, the missions can be completed in any order, with no mission having a set time. A short rest can be taken after every mission, which will give you four encounters - Save the Keep, Half-Dragon Champion, and two or more others, depending on how well they go. So the PCs can choose to be keep-based, or to go out into the village, or a mix. The Old Tunnel can be completed with only minimal resources used, by only taking out the rat swarms and hiding and letting the patrol go by, earning each PC in a party of four the minimum of 25 XP.
There's no in-game, in-story impetus to never rest. It's a long night, a long fight, rotating rested troops and tired troops is sound strategy, and just because the party is taking a short rest doesn't mean they aren't helping around the keep, tending to wounds, repairing arrows, and the like.
My take on the module is that it's designed to give you plenty of options for things to do during the attack, not send the PCs through a punishing gauntlet of missions with all their resources spent. It
can be played that way, but it's not the only, or even the best choice. A party that does do that (and survives) is either going to have enough XP to get to Level 3, or be very close to it.
Incidentally, Seek the Keep is
highly variable. It's got a minimum of 600 XP (150 XP per PC), either for avoiding all the checkpoints altogether (in which case, they pick up at least three more NPCs, for a total of 8), or for fighting only the minimum of enemies (eight kobolds in the beginning, and then 1 guard and 1 kobold at each checkpoint). OTOH, max enemies is 8 kobolds in the beginning, 1 winged kobold, 5 kobolds, and 4 guards at each of the three checkpoints, and one random encounter of 3 kobolds and an ambush drake chasing 6 villagers. A party of four surviving that will end up with 437 XP per PC, and probably have little in the tank for further missions. So how one approaches the Seek the Keep mission will have repercussions throughout the rest of the episode. In groups where relatively balanced encounters are preferred, the DM should probably only offer the simpler missions, and/or reduce the number of enemies. Of course, a pure sandbox DM might want to leave nothing unchanged and let the players make their own choices.