I think what curbs the immigration to Spain is its economic situation(15% unemployment rate), plus I wouldn't say that Spain has tough immigration rules. In 2020 11% of of people living in Spain were foreign nationals: https://www.ine.es/prensa/cp_e2020_p.pdf

Out of these 11% only a third were from EU (including Great Britain), 6.5% of the foreign nationals were from Latin America, taking 5 out of the 15 countries from which most Immigrants come from, and the biggest year to year increase in immigration is from Venezuela (39.8%), Colombia (31.3%) and Honduras (29.4%).