You don't know what your talking about. Most people seems to be reading incorrect posts like this.
Its absolutely easy to switch employers on H1. When a H1 employee wants to change jobs, visa is literally the last thing on their mind because its ridiculously easy to find a company who can file H1, especially in tech sector. What you are talking about may be is the L1 Visa which restricts you from moving to different firm.
The biggest myth of 21st century: All H1B employees are paid low wage. Lol! Any H1 employee who is interviewed and hired in US is paid the same wage or more as a regular US Citizen, depending on your negotiation skills. Tech industry is so competitive that employers dont have the luxury to low ball employees. Infact, hiring a employee on H1 is lot more expensive when you factor in the H1 Visa charges. It costs more than $20K if they need to apply for Green Card.
Companies like TCS, Infosys have positions which pay upwards of $200K. If they pay 65K for a position, it simply means that position deserves only that amount. They pay the same even of they hire US Citizens.
Just because the software firm you are working for is paying you less than what Google pays their employees doesn't always mean your employer is low balling you. Every company has a different structure and different needs and goals. If you need more money, go join Google/other high paying firms. This applies equally to both US Citizens and people on Visas.
Again, H1 employees have ALL the freedom and ease to switch employers.
Avoid spreading fake news.
Thanks.