Re: Off topic, but...
Based on my prior involvement with legal and regulatory data submissions:
Is there someone sitting waiting in an office, staring at their phone, waiting for Google to call?
Normally no, because most documents are emailed or couriered in hard copy. If you're trying to be obstructive you always send hard copy, because its not electronically searchable (and if the recipient scans it, they have to take responsibility for proofing and errors in scanning). Up against a deadline, there will be somebody responsible for monitoring the receiving email address, or on post room duty to receive documents, if need be in unsocial hours, but nobody senior will be leaping on the documents at three in the morning, shouting "let's get to work!".
Do Google have the number of the exact person, and does that person never sleep?
See above. Sometimes the recipient is named, but often it for the attention of a particular post-holder or the head of the regulator. All you need is 24 hour cover on reception/security to sign for hard copy, and an email system that time stamps the arriving email.
What is the advantage of leaving submissions of this sort to the last minute, and what is the incentive for the party (in this case the court) to allow submissions out of office hours?
If the company is expecting to be given a kicking, then by delaying they put that off and buy a few more days for their own legal team to invent excuses or find legal loopholes, but mainly to review and re-review the submission to try and avoid any problems. With a complex regulatory investigation, the inquisitors' ask for a lot of commercially sensitive information, and there's ample opportunity for letting slip things that you'd rather not tell, or opening new lines of inquiry. In the recent UK investigation into energy suppliers, they had to tell the regulator what profits they made by customer segment - whilst they can't lie or withhold requested data, they wouldn't want to give away anything they don't have to, because it is embarrassing enough to admit that its all your poorer customers who are the most profitable, but you really wouldn't want any additional and unrequested detail to slip out that showed the companies were intentionally milking that segment.
One major driver of last minute submissions is also the complex nature of court or regulator's questions, the job of writing, collating, multiple levels of management review, then legal and board review, all of which mean that its usually rare to be able to make a detailed regulatory response early.
There's no particular incentive for a court to allow unsocial hours responses, it depends whether the original requirement specified anything about when the response could be returned, which might be "no later than 29 July", which by definition goes up to 23:59, or it could have demanded "by 17:00 on 29 July".