The problem is that a solar sail has a fixed amount of mass per unit; for a 2 mil metallized Mylar (PET) sheet, the area mass density about 70 g/m2. That may not sound like a lot but given that solar radiation pressure at Earth orbit is ~4.5⋅10-6 N/m2, the maximum possible acceleration of the solar sail by itself is ~6.4⋅10-5 m/s2, or 0.0000065 g, which is not enough to even escape Earth’s sphere of influence without additional propulsion. At the orbit of Mercury the radiation pressure jumps up by around a factor of 10 (depends where the planet is in its orbit because of the eccentricity of e=0.205) so you can knock that down by one zero, which still is about the same amount of acceleration as staring at someone really hard across the room.
Of course, once you start adding any significant payload (i.e. anything larger than a CubeSat) the amount of surface area necessary to get anywhere becomes literally enormous because the mass fraction of the payload has to be tiny to even get and acceleration within the same order of magnitude as the bare sail, notwithstanding all of the structure necessary to keep the sail relatively rigid and transfer load to the rest of the spacecraft which it is pulling along. If you had a spacecraft with a payload mass fraction of 0.1 and a total mass of 1000 kg, the solar sail would have to be almost 13000 m2 to get an acceleration of 0.00000585 g at Earth orbit; big and awkward, but within the range of feasibility. For some minimum spacecraft that could potentially carry a small crew of humans to Mercury—say, 1000 metric tons—it would have to have a solar sail of almost 150 km2 and all of the associated structure to support it, and it would take a few decades to get from Earth to Mercury, so the spacecraft would somehow have to have essentially 100% recycling of food and water because the mass of consumables that would be required would dwarf the rest of the ship.
For what it is worth, years ago I worked on a proposal effort to develop solar orbiting satellites to provide communications and positioning systems for interstellar missions, and one of the things we looked at were membrane structures for both solar electric power and solar propulsion for stationkeeping. At the time the state of the art of ‘inflatable’ solar arrays was still in its infancy and we ended up eschewing that for onboard nuclear reactors (which killed the proposal since that was never going to happen). Today, deployable solar arrays of a few hundred square meters would be feasible. Station-holding using solar radiation pressure, however, was a complete non-starter, a conclusion I initially disagreed with until a more experienced engineer walked me through just what it would take to build, test, and deploy the required several square kilometers of sail area, and how much mass that would add to a payload that was already pushing the capability of the Delta IV Heavy. Solar sails are great for small payloads that can spend many years languishing between planets, but they don’t scale up to larger payloads or crewed missions well at all.
Stranger