Is it safe/reasonable to just keep consuming more?
Yep, that's the right move.
The reason why is there is not a linear relationship between physical activity and daily calories burned.
After a certain point, the body will compensate. Say you're extremely active. After 4 to 500 calories of physical activity (we're not including calories burned from just being alive i.e. sitting around), while you will continue to burn more calories from that physical activity, your body will compensate somewhere else.
For example, you may burn extra calories by walking around more due to that extra energy you have. However, when you sit down, you might no longer do this as much:
This is why you'll find people who use a standing desk during the day do not automatically burn that amount more calories on a daily basis. While they may stand more at work, they may balance that out (to some degree) by sitting more once at home.
(And no, you can't get around this by moving around all day. The body can slow down other processes out of conscious control. This is why extremely active women, even if eating ad libitum (no eating restrictions), will lose their period. The body shuts down that highly metabolic process due to all the necessity for metabolism elsewhere.)
On the left is what we've long thought happened. On the right is what actually happens,
Notice how this line levels off as physical activity goes up. You get less and less caloric burn despite more and more physical activity:
More thorough discussion of this phenomenon.
Long story short: keep consuming more calories. At some point, the calories in will outweigh the calories the body will burn, almost no matter how active you are.
***Note:
Whenever I discuss this I often get people with a rigid mechanics mindset jumping in with "THAT VIOLATES PHYSICS!!!" Just to reiterate, no, it does not. It is perfectly consistent with thermodynamics.
Again, if you are active, you do burn more calories from that activity.
However, the body will find other areas where it can burn less calories to offset that activity.
And for those saying "Oh yeah, what if I run for 24 hours?" Well, how many days in a row are you going to do that? And just think about a marathoner, what do they typically do the week, or month, after the race? They sit around, a lot.
What do people do after they drink a bunch of caffeine? They jolt around for a while, but then they typically crash, moving a lot less.
You have to view this outside of a single hour. Think in terms of days, weeks, months.
