Yeah, at this point controlling the border means changing the asylum process, and as both Trump and Biden have demonstrated over the past 6+ years, there is only so much the Executive can do without any new LAWS that govern the asylum process. There’s also international law to consider, but at the very least Congress should be fixing the asylum process.
Catch and release is a version of border control—we should really want those lawfully seeking asylum to present themselves at a port of entry, while ensuring those who illegally enter (meaning not presenting themselves at a port of entry) are permanently at the back of the line. The problem is the amount of time it takes to process asylum requests, the backlog of cases, the lack of judges/manpower to fairly adjudicate the hearings. It provides a disincentive for lawful entry—why do that when I can take my chances with the coyotes and just disappear into the country?