Reaching orbit with a pressure fed engine is really tough because of the need of high thrust and to achieve high thrust, high combustion chamber pressure is needed. And hence the pressure, at which propellants are stored, have to be very high leading to very high mass of the propellant tanks.
Because of the above reason pump fed engines are being used till date (23/11/2018) which reduces mass and require less propellants to reach the orbit compared to pressure fed engines.
For small thrust requirement (like thrust vector control, orbit change, etc.), pressure fed engines are the best option because it reduces complexities in making pumps & turbines system and are quite compact in size.Now companies are coming up with pressure fed engine but just for the last stage where they have to do minute corrections in trajectories.
Armadillo, Masten, XCOR, etc. are companies who have made landers and are low in mass and hence require less thrust. Because of which they are able to use pressure fed engine. And most importantly these landers are designed for the moon where gravity is less and requires lesser thrust to lift-off the same mass than the earth.
In recent times, a lot of new student space programs are coming forward, like SDSU, dareTuDelft, USCLPL, etc. (get to know more on this website), who are using liquid propellants and pressure fed engine system.
Finally, by the increase in material research, to find better material in strength to weight ratio, making a launch vehicle with just pressure fed engine system is not impossible in near future.