Why would you wait a year to start the ball rolling, unless your client doesn’t want the money soon and likes the interest rate that the government pays?

Amended returns go to a gatekeeper. Most are just passed along for routine processing, which can take about the same amount of time as an original paper return – sometimes less than the 45 days when interest becomes due. Others are sent to Exam, which generally works them in the order received. (Actually, that initial determination of audit potential is reviewed two more times.) Those are the ones that can take months. It’s possible that the more IRS catches up on the backlog, the more closely these "CAT-A" claims will be examined.

The procedure is described in a TIGTA report from 2016:

Current IRS policies and systems only accept amended returns via paper returns. The paper
returns are first received by the Submission Processing function, which is part of the IRS’s Wage
and Investment (W&I) Division. Tax examiners manually review the claims to determine if they
meet certain criteria (i.e., Category A, which is often referred to as CAT-A criteria) requiring
additional review. Claims that do not meet the CAT-A criteria are processed within the
Submission Processing function and thus are not forwarded for possible audit. Those claims that meet the CAT-A criteria are referred to the IRS’s Accounts Management function. Once the
Accounts Management function receives the claim, it is responsible for confirming that the claim
in fact meets CAT-A criteria and was not forwarded in error. If a claim meets CAT-A criteria,
the claim will be forwarded to the Campus Examination Classification function, where it is
reviewed to determine if the IRS should select the claim for audit.