We've had examples where it looked like someone was going to catch something but didn't.
Take Snivy's capture for example. While it would've been stupid, the episode could've been easily done with no capture in the end. Just like with that Jigglypuff episode in Battle Frontier, Ash could've realized it wasn't right to keep attacking Snivy, since it obviously didn't want to come with him, apologizes and say goodbye. If that happened it would've just been like your example of without the egg, and then the episode would've been pure filler.
But everything that happened in the Snivy episode directly was the reason Ash caught Snivy. Snivy found a perfect trainer.
It doesn't matter if a certain scene doesn't impact the episode at all. Like Ash saving a Pokemon and then it ultimately decides to go with him. Saving that Pokemon has no impact on an episode's plot, but it would be the reason why said Pokemon decides to go with him. Oh right I almost forgot, for you saving a Pokemon is a bullcrap reason for a Pokemon go to a main character.
It's the same case here, Ash volunteered to help the Yuri keep the kids in order, or at least reason with them. Because Ash did, and helped greatly, the daycare woman rewarded him with the egg.
I mean sure I'll agree that the episode could've been the same without the egg, but because of Ash's action to the episode's plot was the reason he got the egg. He didn't get it because he was good looking, he did it for helping more than Iris or Dento.
In this episode one of the main COTD's was the daycare lady (caretaker), and showed Ash, Dento, and Iris the eggs prior to going to the school. Obviously the caretaker was good friends with Yuri otherwise she wouldn't have been in this episode or most of it anyway.
So someone receiving the egg isn't without possibility.
A better example to your "the end means nothing to the episode" argument is this:
The episode is about Shinpora, Ash helps out Shinpora and there are some nice scenes where Ash and Shinpora bond. Ash then says goodbye to Shinpora and Shinpora happily says goodbye (because it made a new friend, or whatever), then near the end Ash, Iris, and Dento are walking along and then a Bachuru appears out of nowhere and attacks Ash, thus Ash battles it and captures it and the rest of the episode is Ash, Dento and Iris confused as to what just happened, then Ash shrugs his shoulders and says "Alright I got a new Pokemon."
That's a perfect example to your argument. Bachuru just appears out of nowhere, didn't even show up in the episode until the end. That's something I'd be willing to say was filler-ish because it popped out of nowhere and it's capture didn't impact the episode's plot with Shinpora at all.
Unlike this episode where the episode's plot is the reason Ash gets the egg in the first place, just like any normal capture episode.