I actually made that thought experiment. Disallow selling businesses. Disallow selling shares. Disallow stock market. Disallow mergers. The only way to acquire a business is to found it or to inherit it. The only way to quit a business is to shut it all down, with all assets liquidated, all liabilities settled, and all contracts terminated.
The main downside is that it's harder for to make money. Otherwise... I only see positives. And no, it wouldn't kill innovation. The investors would just have to invest the old fashioned way - by founding companies or expanding their existing businesses. As for job security, we already don't have it in the current system.