Reality is, they do displace workers, but over the long terms costs go up due to lost customers and revenue and the need to replace those workers with competent unsourced individuals (happening a lot over the last 3-5 years).
This is not speaking to the general H1B individual, only those that places like Tata and IBM have been hiring to "offshore work" and "reduce costs"; and those same companies slowly lose enterprise customers fed up with the lack of quality.
HP was another company that took on contracts providing corporate IT services, outsourced them and then found customers firing them and then insourcing talent.
A Tier 1 migrant in the UK has total freedom over who they can work for. They are not tied to a particular company and as such can leave for a better job without any administration overhead for them. They also have the ability to start their own company without any restrictions. This places them on equal footing with any local job applicants as they cannot be forced to work for lower than the industry going wage.