The Mexican central bank, by contrast, warns that remittances are a very dangerous crutch to rely on for Mexico's development. That's right, the Mexican central bank.
I wouldn't challenge their opinion. Remittances can be cut off any time. Their best workers are in the US, not building anything long term for Mexicans.
She didn't say this money was from illegals. However, to address that chance, a good revenue raiser might be to have banks require a green card or proof of citizenship (birth cert) or naturalization papers before money can be wired outbound for no cost. If these documents are not present, the US govt could charge $10 per $100 wired. The proceeds could fund the fence.