To have really capable people work on breaking your crypto for free, you have to be an insider. You become an insider by breaking other people's crypto. You can publish a break in an insider's crypto even if you are unknown. After you publish a few such papers, you become an insider and can publish your own crypto other people will spend their time trying to break.
People can learn the state of the art and develop an alternative to the common (NIST) choices which are no worse, but also no better. Some of those are blessed as "national pride ciphers" (GOST, Camellia, SEED, etc.).
Making a secure encryption algorithm requires a lot of presence of mind, and a lot of industry knowledge. If your threat model is incomplete, you lose. If you forgot one tiny thing at one tiny point in the algorithm, you lose.
If you don't have people checking your work, how do you know? If someone is determined to break your encryption, they are capable of spending a lot more time analyzing it than you spent building it. And they only need to find one mistake.
It's definitely better to use the tools that experts have spent lots of time, lots of breadth of knowledge, and lots of depth of knowledge inspecting.
A better question to ask is, how easy is it to break the protocols and the software using the protocols? We have secure ciphers. Those aren't where the problems in computer and network security lie.
Is there a general way to attack naive ciphers?
I fall of at even a proper Vigenère cipher, although I guess I could hack together a terribly inefficient python script to test all options and then print them line by line and start visually scanning for patterns :-/