Bitcoin would more likely then not be less expensive then 2%.
This price does sound low for moneygram transactions. Are they not instant transfers?
Yes, it's an instant transfer. Although, admittedly, I pick up the money only after 10-18 hours because of time zone differences.
On moneygram's site, when I click on "estimate fees",
it currently shows only a 1.6% fee to transfer 1000 USD from my client to me.
With such low fees, I have little or no motivation to find a cheaper alternative.
Ten years ago, when western union was the only option we had, I recall the WU instant transfer fee was approximately 10% !!
USD to USD transfer is cheap.
For people doing non-usd transfer, that is when bitcoin shine because currency conversion fee alone is usually 2-3%.