can you evade a lawsuit by making a small breach, which is forgiven, then wait 4 years and then you can breach it all you want because the first breach already occured?
No. Those would be separate breaches of one same contract, and the statute of limitations operates individually for each breach. The waiver of legal action pursuant to the first breach, such as where the injured party lets the statute of limitations expire, does not forfeit filing suit for breaches for which the statute of limitations has not expired.
Even if a party repeatedly breaches one same clause, the injured party can sue for all the breaches for which the statute of limitations has not expired. The fact that those breaches are similar in nature does not tie them to the same deadline for commencing court proceedings.
Is the statute of limitations fairly irrelevant?
No. It is important to distinguish between the date when a breach occurs, and the duration of its harmful effects. The statute of limitations relates only to the former (i.e., the date) even if the duration of its harmful effects coincides with the contract remaining in its breached state.
The reason of being, or one main reason of being, of the statute of limitations is the premise that the parties' memory fades over time. The persistence of harmful effects does not necessarily imply that the defendant and third-parties/witnesses remember the circumstances of the breach. And the greater the delay in commencing court proceedings, the likelier that the defendant and non-parties has disposed/eliminated evidence with which the defendant could dispute the claims or charges. In theory, such factors put the defendant at a disadvantage insofar as these impair his ability to defend & prove his position.