I think Beckham presence on the field does make a difference. A lot of times you would see him connecting forwarders and defense players by smartly distributing the ball between them. Also practically all the goals from FK and corners are assisted by him, which makes it another major plus.
Yes, he might not be multi-dimensional, but that does not mean he is a bad player. I think he is also a great team captain. He knows how to inspire, how to create and how to comfort when things go wrong. He does the job just fine.
I have seen him perform closely since 1998 and I noticed that his game gets lifted in critical moments. He is there to mastermind the attack and his foot is there in defense when its most needed. He is noticed, that's for sure. And with his FK taking abilities, he doesn't need to be a player.