SQS limits you further in other ways. For instance, scheduled tasks are capped to 15m (delaySconds knob), so you'll be stuck when implementing the "cancel account if not verified in 7 days" workflow. You'll either reenqueue a message every 15m until its ready (and eat your the SQS costs), or build a bespoke solution only for scheduled tasks using some other store (the database usually) and another polling loop (at a fraction of the quality of any other OSS tool). This is a problem well solved by sidekiq, despite the other drawbacks you mention.
Bottom line, there is no silver bullet.