I'm not sure it's a house rule. I truly am not sure it would not be allowed. As I said there is nothing to indicate you can't fill a prepared spell later such as when you gain a level without taking a long rest. I don't know that most DMs require a long rest to level. I know I don't. I require a bit of down time, not even a short rest. I do allow a player to fill an opening in their prepared spell list during that short time. That made me think, "Would I allow a player to prepare a spell if they left a couple of openings on their prepared spell list?" I read the rule for preparing spells and decided there is nothing specific stating a player can't leave a few openings on their prepared spell list and prepare them later. The only clear text is that once a spell is prepared, it can't be changed until a long rest.
DMs should ask themselves if a player chose to prepare eight spells of a possible ten, would you allow that player to prepare two more spells at a later time to reach the maximum prepared spells allowed? My answer to that question was yes. I did not think the rule text indicated that ruling was wrong.
I was looking at this from a DM perspective if a player told me he had done this. Would I unequivocally rule that he had to prepare spells at a certain time and once he had done so, he could not do so again until a long rest even if he prepared fewer spells on purpose. I also asked what if the caster was interrupted while preparing spells? Would I then not allow him to fill those prepared spell openings at a later time? My answer to that question was no. I would allow him to prepare spells at a later time if interrupted during an attack.
I was sifting the rule using scenarios where a player for some reason did not prepare all the possible spells he could during a particular period between long rests. I could not find a good reason why he could not prepare a spell if he had for some reason not prepared his maximum amount. I guess most posting on here can answer the same questions with an affirmative no. I cannot do the same.