Thats really interesting - I have 578 nights now so soon getting a good LT status but I wasn't aware that someone needs to stay every night in a hotel to get a credit as it would otherwise violate T&Cs.
I can remember at least 2 nights during my younger years working as a consultant on week long engagements and staying in Marriott hotels, but for reasons I cannot explain further I ended up on some Thursday nights staying over in different places
Paid the whole stay though - always thought that's what counts...