You make a very good point that the current ideal of "employment" is relatively new. Interestingly, history may be repeating itself. Freelancers who specialize in one field or sub-field occupy a similar niche to craftsmen from earlier centuries. For example in colonial New England, it was common for people to specialize in one craft (blacksmithing, cobbling, etc) and train younger generations through apprenticeships. Nobody called this "entrepreneurship" or "freelancing," but that's effectively what it was. Small businesses and enterprising individuals traded their labor to the local market in exchange for currency.
Human beings and societies can adapt to market changes much faster than regulation or measurement can catch up to them. Hopefully the US government begins to realize the efficacy and prevalence of these "alternative work arrangements" (I'm also not a fan of the term), and implements policies that consider them. Some things I'd like to see:
1) Better tax treatment (freelancers who setup an S-Corp may end up paying more tax than if they were an employee, since they need to pay corporate income tax, personal income tax, and in some cases payroll tax)
2) Better / more nuanced measurement of "unemployment" in the country. It's an open secret that the unemployment models are a complete joke for a number of reasons. One is that they do not accurately consider contractors, and another is that they consider someone who has "given up" on looking for a job to be "employed." The models are designed to make politicians look good, which is fine... except when the market starts moving based on the models. That is bad.
3) NOT funneling contractors into employment arrangements. There are many advantages to being a contractor (flexible hours being the major one), and if government regulation forces companies like Uber to treat their contractors as employees, these advantages will rapidly disappear.
4) Better treatment of 1099 workers / freelancers / small business owners when applying for loans or mortgages. Banks are generally very unwilling to lend money to a "freelancer" and often want to see more years of history than they would require from a salaried employee. This seems like laziness on the part of the banks, who are unwilling to develop risk models for freelancers.
5) More willingness from employers, government or otherwise, to consider ex-freelancers viable job candidates. Many firms will throw out resumes from freelancers under the assumption that they are a "bad employee" (too independent, can't follow instructions) or the freelancing was an exaggerated description of unemployment.
There's lots of problems with how this class of workers is treated, and addressing some of the above will hopefully go a long way toward welcoming them into society.