There have been efforts by all presidents over the last 20 years to do so.
Obama increased the rate of deportations and doubled border patrols as part of a gambit to reach consensus on immigration reform. Congress didn't take up the offer. https://obamawhitehouse.archives.gov/blog/2013/01/29/preside....
Trump (first term) put forward reforms that never passed the Senate (https://en.wikipedia.org/wiki/RAISE_Act).
Biden late in his term put forward an immigration reform package that Trump, as a candidate, guided his party to reject. https://www.factcheck.org/2024/02/unraveling-misinformation-...
The US Congress is not an effective institution. It is captured by lobbying dollars. And the specific geographies each member represents in the House of Representatives have been organized to create partisan (far-left/far-right) districts that don't elect middle-ground candidates. Congress is more partisan than the country in general and also corrupted by financial influence. By design, the US Congress requires broad consensus to operate (bills need to pass the house, the senate, and then be signed by the president; to pass the senate, many bills need 2/3rds approval in practice). Congress has been largely unable to reach this broad consensus (on many issues, not just immigration) over the last many years.