The egglay is also effective vs enemies with a much better ground game than air game (Snake).
The egglay is good against enemies with low priority down airs (Kirby).
In team battle, and trust me, this will happen VERY rarely, the egglay can be used to give them an extra boost if team attack is on, without threatening them with an out of screen experience.
The egglay is a hardcore mindgame because it has shorter range than yoshi's dashgrab. An opponent may dodge the egglay a few times, only to get dashgrabed later cause they thought "That was your grab...."
The egglay edge pull works amazing wonders against Snake. Seriously, you WILL pwn him if you can do it. Either the pull works and he's sucked under the edge, or you accidentally swallow him, however, the momentum from the egglay will cause him to stall in the air for a second if he goes immidiately for Cypher.
You can egglay through Mach Tornado. If you can get metaknight away from that move, more power to you. It also wins vs his dash attack, and outranges his downsmash.