The passenger ferry terminal is a few minutes' walk from the pier, boats run frequently, and the crossing to Playa del Carmen takes roughly forty-five minutes. It looks, from the deck of a ship, like an obvious way to see the mainland. It is the single most reliable way for a cruise passenger to miss all-aboard on Cozumel.
Count the pieces. Forty-five minutes across, a queue at each terminal, whatever you actually came to do, forty-five minutes back, then a walk or a taxi back to the ship. That is most of a call before anything goes wrong, and the things that go wrong here are specific and real.
Weather closes the channel. Between roughly mid-November and mid-March, a norte blows down the strait and the port captain suspends sailings. It can happen with a few hours' notice and it can last more than a day. If it happens while you are on the mainland, your ship leaves without you and you are arranging your own way to the next port from a foreign country.
The ships do not wait for independent travel. That is the entire difference between a ship-sold excursion and one you booked yourself. On a mainland trip that difference is not a technicality.
If Tulum, Xcaret or Playa is the reason you booked this cruise, buy the ship's excursion and let them own the risk. If you are on Cozumel for a day, spend it on Cozumel; the island has a better reef than the mainland and a fraction of the coach traffic.