Earth's orbital velcity is ~30km/s. So by extension, anything that comes from Earth will at least have that speed. So the probe needs to find 30km/s delta v in order to actually get close to the sun.
I don't understand why we aren't doing solar + ion drive everywhere (except obviously launch), and instead we settle for slow multi-year multi-grav-boosts trajectories. Current ion drives (by NASA and on Starlink) have 2500-3500 Isp. Which means that even 100+ km/s is easy doable with just 2 stages.
The Parker Solar Probe mass is 555kg. An achievable amount of ion thrust is around 0.5N. Thus, running that thruster would accelerate the craft at 0.0009m/s2.
Getting such a craft to 30km/s of delta-v would therefore take about 33.3 million seconds of thruster time, or about 13 months.
I don't know what the duty cycle is on ion thrusters. Maybe they aren't robust enough to fire for over a year straight?
To be precise for 555kg probe you'd need additional 600-800kg of propellant mass and thus run the thruster(s) at about 1.5N thrust using 40-60KW - 250m2 of solar panels - everything is available at the current state of tech.
https://en.wikipedia.org/wiki/Ion_thruster
"A test of the NASA Solar Technology Application Readiness (NSTAR) electrostatic ion thruster resulted in 30,472 hours (roughly 3.5 years) of continuous thrust at maximum power. Post-test examination indicated the engine was not approaching failure.[75][3][4] NSTAR operated for years on Dawn."
In that case I have a theory. The extra propellant mass, extra solar panel mass, etc, are all more mass against a small amount of thrust. Every bit of additional mass extends that 1-year timeline, and all the extra stuff is extra things that might go wrong.
So instead of a 7 year mission being reduced to 18 months, we have a 7 year mission reduced to maybe 4 years, but then there's possibly a higher chance of failure.
Balancing three years against failure risk, I could see that falling on one side for some missions, and the other side for others. I'm not surprised that they pick the extra time for some missions. I am surprised that they don't pick the faster option more frequently.