This summary is not the rule. The rule text controls.
Lawyers can't agree to limit their own right to practice law in the future, even if they want to. This means a law firm can't ask a lawyer to sign a contract saying they'll stop practicing law (or won't compete with the firm) after they leave, quit, or get fired. The only exception is for retirement plans, where a lawyer who is genuinely retiring can agree to give up practicing law as part of getting retirement benefits.
The same rule applies when settling a lawsuit. If a lawyer represents someone suing a business, the business can't offer to settle the case only if the lawyer agrees to stop taking similar cases against them in the future. This kind of deal is not allowed, even if both sides want to make it.
The reason for this rule is simple. Clients need to be able to choose their own lawyer. If lawyers could be bought out of practicing law, it would limit choices for future clients and could stop good lawyers from taking on cases against powerful companies or firms. This rule protects the public's ability to hire the lawyer they want, not just the lawyer that opposing sides allow to be available.