If he forces major companies to provide access to their data, that still leaves minor companies or open source projects to do what they want and therefore still

If he forces major companies to provide access to their data, that still leaves minor companies or open source projects to do what they want and therefore still leaves the bad guys with a place to hide. The only alternative is to ban encryption for all but those who agree to allow access by the government (with a warrant of course) which while possible is highly implausible given how much internet traffic is currently encrypted.