The problem with deliberately triggering false alarms is that users will at some point lose trust in the AV software. The rates of false positives are also an important factor in AV rankings - and these rankings potentially influence users' buying decisions.
So legitimate AVs will probably offer you potentially unnecessary bonus features rather than pretending there is a concrete dangerous infection that can only be fixed with an expensive upgrade. (Software that constantly warns about non-existent threats would get into the realm of scareware.)
How important good detection rates are for an AV company's reputation shows the reported story from 2015 that Kaspersky employees had submitted mocked records to VirusTotal to trigger false positives in competing AVs:
Two former Kaspersky employees have accused the company of faking malware to harm rival antivirus products. They would falsely classify legitimate files as malicious, tricking other antivirus companies that blindly copied Kaspersky's data into deleting them from their customers' computers.
That said, many AV companies have been criticized for unethical behavior. E.g., Symantec (the company behind Norton Antivirus) has been alleged of charging unapproved extra fees and pretending "remove" non-existent malware:
Symantec has been criticized by some consumers for perceived ethical violations, including allegations that support technicians would tell customers that their systems were infected and needed a technician to resolve it remotely for an extra fee, then refuse to refund when the customers alleged their systems had not actually been infected.