I see the implementation of cryptosystems as an engineering endeavor little different than designing, for example, a commercial airplane, a bridge, or a radiation therapy machine. In all cases you have a system whose failure can result in anything from monetary loss to death (for an example of the latter, faulty cryptographic software used by dissidents in repressive countries). In all cases you use a combination of rigorous testing and analysis from first principles to try and isolate potential weaknesses. In all cases you want to ensure the people who worked on the system knew what they were doing and put the right amount of due diligence into ensuring the system works correctly.
Unfortunately, not even widely used, highly trusted implementations work right all the time. A out-of-bounds memory bug introduced by an insufficiently vetted commit opened up a serious flaw in OpenSSL. On a much, much smaller scale, I once had the misfortune of working with an old version of Microchip's PIC18 AES library, which had some serious issues that made it nonfunctional for anything more complex than the toy sample app it shipped with. But with enough exposure these problems are eventually exposed and fixed. Would a world where everyone rolled their own bespoke, ad-hoc SSL implementations be more secure? I doubt it.
In the end, I think there needs to be a cultural shift. People shouldn't be discouraged from building their own crypto for fun and learning, but they should be discouraged from deploying it for any application where real security is required - at least not before undergoing rigorous analysis. One of the first things Dan Boneh teaches in his Crypto I class is that you should think very long and hard before implementing your own cryptosystems (i.e. don't do it), because getting it right is hard, and getting it even the slightest bit wrong tends to make it useless. And when you consider that people's livelihoods (their personal information, their money) and even lives might be jeopardized, taking responsibility as an engineer becomes of paramount importance. Crypto just doesn't lend itself to a "build an MVP, get it working, move fast and break things" mindset.