An easy question to ask: if you are coming over the US southern border, why pay large amounts to a coyote (person who professionally smuggles people) to get you into the US at great personal risk, when you could obtain a home-country passport and come straight over the border legally with no personal risk at low cost? If you are interested in staying long-term, you will still be violating the law after a certain point (and presumably would need to obtain false ID all the same), but the relative risk of the initial journey is significantly reduced.
The only possible explanations are:
1) Most other nations’ procedural and cost burdens to obtaining home-country passports are comparable to what the coyotes charge.
2) The US has established additional barriers to entering the country using legitimate documentation from other nations (e.g., visas that are costly in time, money, etc.).