In addition to companies moving overseas, lost investment and general frustration with the tax system itself it can now add lost future tax revenue. According to a study conducted by Bloomberg most of the $2.5 million people earning money from shared services such as Lyft, Airbnb and other services don't pay taxes. They fall under a $20K threshold that don't require companies to report their income at all. Without tax reform this trend is likely to grow.
The government suspects that $194 billion is under-reported every year. As the gig economy grows so will the opportunities to not report the income. People will earn their income from multiple places and these will fall under the reporting threshold. Under-reported income will likely increase as a direct percentage of labor market transitions.
Antiquated systems leave room for mistakes. Financial information can be reported easily ensuring that revenue is adequately represented. It makes no difference if it is 5K or 25K as the revenue can be reported with the same ease. Those that do not meet minimum thresholds simply don't pay but their amount they make from multiple companies is filed.
As the gig economy becomes increasingly common people will naturally have different small pocket earnings that is difficult to include unless the system becomes more sophisticated. This would mean that the way we view taxation and the kinds of taxes we collect, and on what amounts, would need to change. The same sophistication can be used in better monitoring income from large corporations that skirt reporting requirements.