Asylum claims in Britain are at a record high, with around 111,000 applications in the year to June 2025, according to official figures.
The appeals system currently has a backlog of more than 50,000 and a waiting time of at least a year.
There has also been criticism of the proposed reforms from within Labour, with Maskell saying lots of her fellow MPs were "really concerned".
She said it was important to have a robust human rights framework and described "reordering our relationship with the ECHR" as a "step too far".
Reform UK leader Nigel Farage said the home secretary "sounds like a Reform supporter".
"It's a shame that the Human Rights Act, ECHR and her own backbenchers mean that this will never happen," he added.
Liberal Democrats home affairs spokesperson Max Wilkinson said the government should "focus on processing claims quickly, getting them right first time, and swiftly deporting people with no right to be here".
Enver Solomon, chief executive at the Refugee Council, said rather than deter migrants, the 20-year time frame would "leave people in limbo and in tense anxiety for many, many years".
As first reported in the Times, the threat of the visa ban for Angola, Namibia and the Democratic Republic of Congo comes after thousands of illegal migrants and criminals from the three nations were said to be in the UK.
A Home Office source said the countries were being targeted "for their unacceptably low cooperation and obstructive returns processes".