Never walked it but I would check to see what towns you go through have festivals, etc during that time period. It is Semana Santa and everyone goes somewhere on vacation. I am sure there is also an uptick in pilgrims.
On Palm Sunday 2017, I walked up to the Cathedral in Salamanca just as the procession was arriving in the afternoon.
Salamanca - Albergue Casa de la Calera without reservation but I think it did fill up. If you are starting there, I'd recommend making a reservation somewhere.
Calzada de Valdunciel albergue is small and filled up just before I arrived. I walked on another 6 km with 2 others to the pleasant Casa Saso. That's a private place, so you should check in advance whether it is open. Otherwise it might be another 10 km to El Cubo
Villanueva de Campean - I think there was 1 other person in my albergue, but there was another private albergue in town, with other pilgrims
Zamora - I arrived in early afternoon and easily got a bed at the albergue, but it did fill up. There was lots going on in Zamora during Easter week, and the albergue keeps strict curfew hours, so you might consider reserving private accommodation.
Montamarta - Several accommodation options.
Granja de Moreruela - I don't think the albergue filled up. There was a small procession
Up to Granja, there were maybe 10-15 pilgrims on the road each day. After Granja, though, it dropped to me and another couple, but a day later they took a bus to meet people elsewhere.
Benavente - big town with many options. I couldn't find the supposed municipal hostel (didn't try too hard) and stayed in a hotel.
Alija del Infantado - After a local in a small town invited me to Easter Sunday mass (but it didn't start for 2 hours so I declined), I arrived in Alija del Infantado where 1 other pilgrim was spending the night. We agreed that one room would be for women (me) and the other for men (him) and no one else arrived. Could not find anything open for food (being Easter Sunday) except the Repsol station. My dinner was barbeque-flavoured peanuts and stale Magdelenas, with perhaps the worst wine I've ever tasted.
La Bañeza - I was alone in the well equipped albergue - in a room with about 12 hospital beds, each with a different coloured bedspread. Very bizarre.
Astorga - The approach to the city is confusing, but you'll eventually get there!
So, I was on my own from Granja to Astorga. There were a few navigation questions but nothing I didn't figure out. The weather was perfect and I found the solo adventure and challenges to be fun. My Spanish is reasonably good, which helped a lot.
Most of the Easter events took place in Salamanca and Zamora - they were well worth attending, but reservations might be a good idea.
Was it the most scenic/historic/spiritual route? No.
Would I recommend it - of course! I thoroughly enjoyed it.