I have mixed feelings about this. It could (further) discourage firms from offering their employees specific specialized training which, for some reason or another, are considered important for them to have and which could, absent the security of a non-compete agreement, harm the firm commercially were some employee or employees with very specific, hard-to-acquire skills and knowledge to leave (or be fired) for any reason. It's true that companies and even non-incorporated firms abuse these agreements, requiring them for (no doubt) generic activities, to insulate themselves from competition -- after all, homogeneity in the goods produced and sold is usually one of the requirements economists use to define competition. But, they are unjustified and unjustifiable otherwise, since it gives very highly skilled (and highly compensated) employees an unfair advantage over their employers, raising (further) the cost of employing such people or of training the employees they already have to do that work. Not to mention that it would make protecting perfectly legitimate intellectual property rights harder and more costly.
I dislike and oppose any kind of producerism, be it in international trade (protectionism), in public finance (giving tax breaks and outright subsidies for production, what is usually called "State aid"), in capital markets (for example artifically encouraging investment in this or that sector of the economy), in labor markets (such as banning non-competes, allowing trade union labor monopolies, wage controls, excessive immigration and emigration controls), or in land (natural resources) markets (such as State monopolies on the exploitation of such resources). Producerism is based on the mistaken (and all too common) overappreciation of "making stuff" (industrialism) at the expense of other economic activities -- and it is ofen vulnerable to being used as a cover for xenophobic and other prejudices against social classes or ethnic groups not particularly prominent in the "good manufacturing" sector.