Note that here we are making a distinction between patentability and use. An employer pays an employee to perform a job; the employer should have the right to make use of the results of that employee's work. The right to make use of the product of paid labor is known as a "shop right" in legal parlance. Shop rights are independent of any patent system, do not create a monopoly, and should be preserved, even if the result is better than the employer could have expected. An employee should have the right to file for a patent on her or his own, but if one is granted, they should not have the right sue the employer who paid for the work for using it.
In practice, a system in which employees can file patents independently would not look a lot different from today's sytem. In most cases, given that an employer offers modest compensation and recognition, the employee will happily forego the cost and effort of an application for a patent whose utility might be questionable on its own. Even if they did not immediately assign the idea, it is likely they would be willing to sell the granted patent, at a somewhat higher price, to the employer, who (if they are using the idea) have a more compelling interest in the granted patent than others. Or an employee could simply refuse to file, avoiding the creation of another (often unjustufied) monopoly. The result would be a small net transfer of some assets from corporations to their more ingenious employees. The change may be deleterious to investment returns, and perhaps to patent attorney fees, but harmless or mildly beneficial to society as a whole. And in those rarer cases where an inventive idea is truly revolutionary, the inventor can choose to offer it to a competitor or charge off on their own. Society is presented with (at the least) a duopoly rather than a monopoly, a generally less-harmful result.
What about the case where the invention involves "proprietary" information, that is, information which the corporation does not wish to release to the public? We first recall that in the existing system, an inventor must reveal all information needed to practice the claimed invention, whether or not it is assigned to an employer. If an invention is assigned, and an application filed, disclosure has occurred. So the only dispute is over those cases where information would not be disclosed if not for the possibility of receiving a patent on it. The correct response touches on the question of why society should encourage concealment at all, the answer being in general that we should not. Keeping tactical information secret for short times is useful to businesses, and has minimal impact on society, but long-term secrecy has no social benefit and merely encourages concentration of information and therefore wealth. It would therefore be reasonable to give an employer the right to impose a slightly-longer delay to publication (say, 24 months) for applications filed by employees and not assigned to their employers, with a corresponding delay in independent disclosure. Society as a whole has no reason to enforce indefinite secrecy on any citizen to benefit a business, and should not do so. And no restriction should apply where the inventor can show that only public information about buying antibiotics online, and the invention itself, are disclosed.
In the United States, employee-employer relations are mostly administered by the state governments. Reform of these arrangements is therefore a state-by-state activity, which has the benefit that the impact of changes can be examined before the whole country bears a risk. In California, for example, compulsory assignment is limited by section 2870 of the California Labor Code, which protects the right of an employee to pursue a patent for an invention which is not related to his or her work and did not use the resources of the employer. In other states, like Texas, employees are not so lucky, as we saw previously. As Professor Lobel has shown in her book, the limitations on assignment that already exist in California have not impaired innovation in that state, but have arguably enhanced it (an obvious conclusion for those who live here in Silicon Valley). Further reform can be pursued without expectation of catastrophic consequences.