If you leave out the delimiter, then you also remove all doubt related to thousand-separator vs comma separator. Many countries use comma as decimal separator, so "10,000" could be interpreted as "10 comma 000".
I believe it depends on the circumstances. In general, the delimiter would increase readability, but sometimes the actual, exact number isn't that important.
There was a question about "correct payment in financial forms" a while ago - and in such tasks it's definitely important to get the numbers straight.
In other situations, you just want to know if the number is small, big or huge. Eg. a 4 digits of likes on Instagram is good. It's not that important whether it's 1234 or 7654 (because it's a lot more that my lousy 1 digit of likes anyway... ;-)
It's also possible to increase the "significance" of each digit by using different visual layouts and/or a postfix. Fewer digit, but obviously a higher value. Just like the Stack Exchange sites are doing. Even if I have more digits in the example below, it's easy to spot the king...
Vine uses this method too. By postfixing with "M" and "K", it's easy to identify 1.5M as a higher value than 274.9K. (This can be discussed, but lets just say that it's either intuitive for the user group, or that it's ok with a learning period to understand the convention).
Google could have done the same on their search results. It's a lot easier to read "1,000,000,000" than "1000000000" - but at the end of the day it's really not that important to know whether it's "1000000000" results or "100000" results (you never go beyond the first page anyway). I would be fine with "Wow, you need to refine your search term" and "I bet you'll find what you're looking for at this first page"...