Why did Arrow, unlike the other shows of the Arrowverse, pick a combination of its own individual logos in the Invasion crossover story arc?

It's not so much that they avoid the cross-over reference, it's just more important to the producers that this was also the series' 100th episode and they wanted to celebrate that more.

AccessHollywood

Wendy Mericle (Executive Producer): "The 100th episode is a look back at Season 1, and some of the characters that we've known and loved. And it really is a love letter to fans and it's a love letter to the first season. I have to say, it's just an amazing, nostalgic episode that -- it's going to break some hearts in a really good way."

FlickeringMyth

Marc Guggenheim (Executive Producer):“It is a love letter to the show, it draws on all previous 99 episodes pretty much. Everyone who we could have in the episode, from a scheduling point of view, is in the episode. Even the people who we couldn’t have, because of conflicting schedules, are represented. At the same time, you’ve got Flash and Supergirl; that’s an enormous amount of fun. Certainly the recruits also play a very large role, an important role, in the episode. I’m really excited about it.”

EOnline

But executive producer Marc Guggenheim says that in addition to the extra superheroes in attendance, the hour will also pay tribute to the work of the Arrow cast and crew over the past five years.

"The challenge was we've only got 42 minutes and it's the middle part of a three-part story, and at the same time it's the 100th episode," Guggenheim say

I think Greg [Berlanti] came up with an idea that—I don't want to spoil it—really does allow us to have our cake and eat it too," he adds. "I haven't seen the episode all cut together yet but it has some incredibly iconic moments. It is a love letter to the show. It draws on all previous 99 episodes, pretty much."