People do not use Lucky Egg because it takes the place of the Oh-so-important Expert belt on your pokemon. Your strat would theoretically work, but only AFTER a pokemon is KO'd. After that happens, you'll have a MAD RUSH to get an attacker out because there's a 90% chance your opponent will already have an attacker. Be proactive and get some drawing before the MAD RUSH will start. Also, WHY WOULD YOU NOT USE UXIE?! If your deck is so strept for bench spots, you should cut down ASAP. 1-2 bench spots should be do-able. Don't give me any "I use Lucky Egg over Uxie because I don't use Belt". That would be fine, but UXie is searchable and gets out of clutch situations ON YOUR TURN. Expert Belt is too good of a card to replace on the active for Lucky Egg. Unless you are playing something that spreads or does counters (*cough* gengar *cough*), you should play Belt as your tool of choice.
This advice does not "depend on the deck you are using". This is globally true. Decks should not be so bulky that they don't have room for Uxie... ever. The only deck that really uses its 6 bench spots for important pokemon that I can think of is Arceus... and even then I've seen Uxie played in it after the Ripple Swell. And, once again, you should NEVER EVER play Lucky Egg unless you find a way to cheat the system. The fact that it does not let you draw when you need to makes it a worthless card. This card creates a lot of "I could have used this last turn... but now it is too late" situations. Also, the fact that it replaces Expert Belt, a GAME WINNING CARD, on your active is just absurd.
"Draw" really depends on what you need. Teching in Cynthia is not a bad idea sometimes. This is especially true when you play really easy-to-kill mon (*cough* Great Mew *cough*). You'd be better off relying on Judge for draw than Cynthia just because Judge hurts your opponent. PONT is the best form of solid draw right now. POV is also solid when you don't wanna burn your hand. When you need small but quick draws, play Unown R, Pokemon Rescue, Pokedex Handy910is, Pokedrawer+, and other cards like that. Also, a solid 2-3 Collector, 3-4 Bebe, and 2-1 Uxie line will not hurt by any means. This is what most top decks do now... it is just really good.