I currently work in method development for proteomics, and I think about this all the time. Of
course methods must be reproducible, or the paper largely useless. But lately I've come to disagree that source code should be required.
If the research relies on a piece of "in-house" code, which isn't described, then that's a problem. But the OP is about research where the algorithm is the advance in the field. In a way, the algorithm is the result and not the method (even though the algorithm will probably be applied to a sample problem and the results thereof validated).
Now, if I develop a new method at the bench, you are expected to do the method at your own bench if you want to apply it to your research. This often starts as a pilot experiment just trying out the method, which can take weeks to months, before you integrate it fully into your methods. I don't have to provide a kit which consistently implements the method along with the paper. Certainly once the method gains some traction, an outside company may begin selling kits. Until then, it absolutely should be "the reader's job to ... reimplement the research" - that's an essential part of the process.
Similarly, an algorithmic method can be reproducible even if code isn't provided. Just like with bleeding edge wet-lab methods, if you want to use bleeding edge algorithms you will need to be able to code. You will need to be able to read a description of the algorithm and implement it accurately. The publicly funded result is the algorithm as an idea, and providing that the review process works, you're getting that idea. Later on, if the algorithm gains any traction, someone will implement it in a usable, robust package and more labs will be able to use it.
Finally, it takes significant time and experience to produce (and maintain) code that others can use and expect to work most of the time. That's a waste of time/money for a research lab, and an inefficient use of public funds. If you can't code yourself, leave code production to those who do it well and don't whine that you can't just plug-in whatever hot new method just came out without any effort or proper understanding.