This is a big question that often comes up when people who don't like religion are speaking with people who do, especially the small details. The religious person will point out that a kiddush cup must be held in the right hand and the non-religious person will snort and say something like "As if God's paying attention" or "Do you really think God cares about such nitpicking things?" Sometimes it's more dismissively vague as in "All God cares about is that you be a good person".
Now many times that's really just the person saying "I don't care about the details and I can't imagine a god that doesn't think exactly like me, therefore that god doesn't care either". On the other hand, it does tempt the religious person to introspect. To what extent is God a micro-manager? If my tefillin is off-centre by a few millimetres does He really say "No check mark today" for my mitzvah performance? If I only wait 5:59 after meat before drinking milk, am I really committing a horrible sin?
I think that in order to answer that question satisfactorily, an exploration of the halachic system and its foundation is in order. The foundation part is easy. God appeared to our ancestors at Sinai, presented the Torah, both Written and Oral, and left it with us to guide our lives. What's more, He left it in a hands-off fashion as the famous gemara in Bava Metzia about the excommunication of Rabbi Eliezer makes clear: Lo b'shamayim hi! Once given over to us, the Torah and its ongoing development as a tool of study and practice belong to us. Yes, God gave us a set of rules by which to interpret the Written and Oral Laws but using those rules, responding to new situations and guiding ourselves through history is our task.
But if the Torah is ours then what is left of our relationship with God? For many people, whether they realize it or not, there is very little left. Yes they'll pray to Him three times a day but it's by rote, an obligation to be fulfilled. For those folks the details are part of the routine. You do what you do because that's what you do or because the book says. It makes for efficient halachic practice but isn't very emotionally satisfying. I would be surprised that any OTD's from this crowd leave the path because something more emotionally interactive and meaningful comes along. People want an emotional connection to important things in their lives and if their Judaism is just a series of actions without fulfillment then why stick with it when something better comes along?
For some it's a very strict relationship. God is a mean old schoolmaster up in the sky constantly scanning the schoolyard and hoping for the children to misbehave so that He can write down their misdemeanours in His book and, if He's feeling especially luck, mete out punishment. No question as to why these guys go OTD from time to time. Other than through fear or ignorance of the outside world why would anyone choose to live in such a system? The only question is why it doesn't happen more often.
For others however there is a more nuanced relationship based on what God has actually told us. Yes, He is the Creator and He is the King of Life, the Universe and Everything but it doesn't end there. He is our Father. He did not choose us as the Am haNivchar because there was no one better around or because He was stuck with what He had promised Avraham Avinu at some point. He did it because He loves us like a parent loves a child.
This is a completely different way of understanding how the complexities of Judaism matter. God, having given us a system and one overarching instruction - excel at this system I have given you - expects us to do our best without the structure we have ourselves constructed. He wants us to succeed at His charge and, if it is possible to say such, is pleased when we strive for excellence in Torah practice.
No, he probably didn't specifically tell Moshe Rabeinu, a"h, at Sinai that one must hold one's kiddush cup in the right hand but using the foundation of the Oral and Written Torah along with all the mystical principles that accompanied them Chazal and the later decisors decided that doing that was the optimal way to fulfill the mitzvah. When I specifically choose to hold the kiddush cup in my right hand I am trying my hardest to follow Chazal's lead. This is what God is looking for. And if I lazily hold the kiddush cup in my left hand then it's not davka that I used the left hand that costs me mitzvah points but that I could have done better and chose not to.
And why bother? Because just as my Father has given me life, health and the tools to fufil His will so I as His son have a reciprocal obligation to show my gratitude and to try and please Him. I want to excel because I appreciate what He has done for me and can only pay Him back in that way. The details aren't nitpicking, they're showing love for the Creator of the Universe. It's about trying as hard for Him as He does for us.
Perhaps we need to choose this system more often to practice our details with as opposed to the other two.