Because it doesn't matter. The internet came around from the DARPA as well. When you make something open and transparent, it is built upon, and you have thousands of eyes looking at it.

You can create backdoors, but if it's open to begin with, it's very unlikely it'll pass multiple reviews without getting flagged. Further, the bigger it is, the less chance it'll pass as more people are looking it. Finally, Bitcoin's incentives rewards more by playing by the rules than breaking them.

Note that majority of governmental backdoors exist in centralised, proprietary solutions. In the open source space these are likely rare and in not so well known software (likely targetting a subset of audiences, I have yet to hear of a major case).

At this point, when it comes to open source software and digital currencies, I'd say there's a much larger chance that a shitcoin like Ethereum have governmental backdoors, not due to any "alleged" governmental ties, but rather due to the sheer complexity of the code when compared to the "simplicity" and very small track-record of change in Bitcoin.

Finally, the internet is built on sets of protocols. The best protocols are interoperable and simple. Case in point, SMTP(email). Its their simplicity that allowed the internet to grow at such a rate, and it's their simplicity and openness that makes those "standard" protocols be known to be safe.

Edit: Typo