If the H1B program remains, they need to give foreign workers the ability to switch firms while in the US. Current policy forces them to remain with their current firm, which reduces their bargaining power and puts them at risk of being overworked and exploited. Further, it reduces competition between firms, lowering wages. (e.g. it is difficult for a H1B worker to get another job with a pay raise, so they are stuck with whatever salary they have.)
A study by U Notre Dame (which I cannot find on mobile) showed that H1B visas did not increase innovation measured by patent grants, but did 1) increase company profits, and 2) decrease all salaries at the firm, citizen and non-citizen.
This suggests the true incentive of H1B visas is to increase profits by lowering wages, not to find workers that firms are unable to find as citizens.