Barack Obama kept a Blackberry for almost his entire presidency. He "upgraded" in 2016, as mentioned in the The Verge. Obama's retention of a personal cell phone was against the advice of the Secret Service, as told in the New York Times (paywalled/limited).
The Secret Service reports to the president (albeit indirectly through the Secretary of Homeland Security). The president can replace the Director of the Secret Service with someone who has a more accommodating interpretation of the job requirements. That is not one of the positions that requires Senate confirmation.
There are three main arguments that a personal cell phone is insecure:
It transmits, so a bad actor could use it to locate a president. Of course, that only matters if the president's location is unknown.
It is possible to intercept the transmissions of the phone, which make the conversations insecure. The president should not discuss classified information over an insecure cell phone. But a president also shouldn't be discussing classified information with friends, who are the most likely to call on a personal cell phone.
A cell phone also might conceivably collect information on conversations that occur in its vicinity when it is not in use as a phone. Of course, that applies to every personal cell phone in the president's vicinity. This is addressable by removing the phone from the president's vicinity during classified conversations.
The Blackberry that Obama had fixed the third problem by being massively restricted and observed. No picture taking or music playing. It was just a phone. This also reduced the second problem. It reduced the first problem by disabling the GPS, although it would still be subject to triangulation.