(There is a TLDR at the end of the message if you are lazy)
Well, let's see:
There are roughly 10,000 frequently online people on here
Let's be generous and say 3000 of them choose to have custom backgrounds.
Then, we'd need a minimum of 100 mods ( and they all must be full grown adults) to keep up with demand.
Now, let's say all the mods work 4 hours a day, for $5/hour (again, being generous).
4×5=20, basic math, so $20 for a session for these guys.
Let's say the workers are split into 6 sections, one section for each 4 hour section of the day.
Now already, you need mods with a bunch of different timezones.
But let's say you still go for this, you find 100 people, cool cool.
100 × 20 is already $2000 every. f**king. day.
Now let's be a little reasonable here. Pretend that a few weeks after the feature, everyone who wanted it has it (which is unrealistic, but we'll pretend it's realistic), and the demand is a lot lower.
So now, 75% of the mods are allowed to quit and they leave, now we have 25 mods.
That would still be $500 a day.
Now to sum it up, let's say that we need the 100 mods for the first 2 weeks. That would make 2000 × 14, 28,000.
Now for a month after this it's only $500 a day.
500×30 (rough amount of days in each month) is another 15,000.
Put those together, 43k for such a small feature.
TL ; DR:
If we do all the math necessary and use estimates, it will take around $43,000 USD to pay the mods just for the first month and a half, and $15000 for the following months. So yeah, cool suggestion, but I doubt Imgflip will be willing to pay that much for a tiny feature.