While I haven't used TranferWise yet, I think it's a brilliant idea (and yes, their exchange rates look phenomenal)!
There's also a service called PeerTransfer for foreign tuition payments that essentially aggregates outgoing payments, and buys forex in bulk.
Another cool development in the area is Visa (The Card issuer) opening up their APIs to allow direct Card-Card transfers like with Square Cash when they just started out. Barring regulatory hurdles, this method (Card-Card transaction using the Visa/MasterCard/Amex network) is probably the most efficient way of sending money across currencies.
I do believe H1-Bs were used to pay lower wages (more so because of being tied to the employer for long periods of time in the Green Card Process).
However, in my observations and experiences, the last few years (i.e. the years when H1-Bs were allocated by lottery), due to the scarcity of H1-B visas, employers started paying a premium for employees who already had an H1-B visa and the skills necessary, because they could switch jobs immediately (as opposed to having wait 1+ year to hire someone from abroad and wait/hope for them to get through the lottery).
What made it even better was that thanks to legislation by the Obama administration, your spot in the Green Card line was now portable, i.e. even if you switch employers, as long as the new employer files a green card application, you still retained your position in the line.
As you can see, the theme has been giving more leverage to H1-B employees as opposed to the employers - and that is what the American immigration system desperately needs. In the end it's only going to protect American workers.
The only reason H1-Bs are attractive to employers is because the employee is effectively chained to them (through the Green Card process) - which in the case of employers looking to cut costs suppresses wages.
I think the best solution is to decouple the work visa and green card like Canada - and hand over more control to the employees. It will solve a lot of problems!
Canada also does the Labor Market Opinions/US-PERM Certification in the visa phase instead of the Green Card phase in the US - which can theoretically cut down on the abuse of H1-Bs by companies like Disney via. consultancies.