Protos can be more efficient, more effective, or just plain objectively better than mechs and vehicles in a number of roles. Some examples:
Scouting/Recon — A Mist Lynx Prime gets one Active Probe moving 7/11 onto the field for a 150-ton mech cubicle and 880 BV2. Five Satyr protos get FIVE Light Active Probes moving 7/11 onto the field for a 50-ton proto cubicle and 665 BV2. Not only are the Satyrs more efficient logistically and in terms of BV, but with five Probes, they’ll sweep a much larger area of enemy hidden units in a much shorter time than the Mist Lynx. And the Satyrs risk less of the total force when those hidden units pull an ambush on a Satyr.
Spotting for Artillery — Similarly, an Icestorm mech gets one TAG onto the field for a 150-ton mech cubicle and 728 BV2. Or an Asshur vehicle gets one TAG onto the field for 930 BV2. But five Satyr 4 protos (my only canonized design) get FIVE Light TAGs onto the field for a 50-ton proto cubicle and 545 BV2. Although the Icestorm and Asshur are considerably faster than the Satyrs, the Satyrs can threaten five times more targets each turn with TAG-guided Arrow IV Homing missiles than the Icestorm or Asshur, in addition to being more efficient logistically and in terms of BV2.
Anti-Infantry/War Crimes — A Piranha mech can deliver 12 Machine Guns for a 150-ton mech cubicle and 998 BV2. Six Siren 2 protos can deliver the same number of Machine Guns 100 tons of proto cubicles and nearly half the BV2 (516). The Siren 2s are also slightly faster than the Piranha and can come at an infantry formation from six directions instead of one.
Mobile Combat — A Nova Prime can move 5/8/5 and fire seven ER Medium Lasers (six if jumping) per turn without overheating for a 150-ton mech cubicle and 2663 BV2. Seven Roc protos also move 5/8/5 and fire seven ER Medium Lasers per turn for 100 tons in proto cubicles and 2352 BV2. Not only are the Rocs more efficient delivering mobile ER Medium Laser firepower than the Nova Prime, but they’ll last longer. Seven Rocs are much harder to hunt down and disable than one Nova Prime.
Fire Support — A Hachiman vehicle can move 4/6 and throw 40 LRMs each turn for 1484 BV2. Five Gorgon protos also move 4/6 and throw 50 LRMs each turn for 1475 BV2. Not only do the Gorgons throw 25% more LRMs than the Hachiman for the same BV2, they’ll last a lot longer. Five Gorgons are much harder to hunt down and disable than one tank.
Crit-Seeking — An Arctic Wolf can throw 30 SRMs per turn without overheating for a 150-ton mech cubicle and 1330 BV2. Seven Orc protos can throw 28 SRMs per turn for 100 tons in proto cubicle and 1274 BV2. The Arctic Wolf is a little faster and can fire for a couple turns longer than the Orcs before running low on ammo. But the seven Orcs are a somewhat cheaper way to field a mass-critting capability for cleanup or ambushes, and will be harder to hunt down and kill than one Arctic Wolf.
Restricting Movement/Blocking/Fixing Enemy Units — Six small, fast protos like the Cecerops can completely surround a ground-bound mech, forcing it to waste time, firepower, and movement fighting its way out. And they do it for 86 BV2 each. By comparison, even the lowly Flatbed Truck (Armor) will cost 117 BV2 each for the same job, and they are much slower and easier to disable than the Cecerops.
I’d also argue that the Society introduced some new proto capabilities that are difficult, if not impossible, to replicate in other units. The Boggart is an incendiary skirmisher par excellence. And the Basilisk Quads deliver a unique electromagnetic physical attack.
So even if there was evidence that protos and their pilots are harder/costlier to field than similar mechs/vehicles and their warriors/crews, it would still be worth it in terms of logistics, BV2, or just plain mission capability to go with the protos in many cases.
That said, there are mech and vehicle roles that protomechs have lots of difficulty filling.
Although their numbers and mobility make them hard to hunt down and disable, a couple protos cannot hold ground or static positions like a mech or even certain types of infantry/BA.
Similarly, if you need to go through a wall/building/fortification/target — not just around it — the size and physical capabilities of mech are clearly superior to protos.
There are a few protos that field ER Large Lasers or Heavy Medium Lasers for ten-point hits, usually at some questionable sacrifice in mobility or armor. But you can’t beat Gauss, Clan Peepers, Heavy Large Lasers, and 20-class ACs for 15+ point hole-punching, and these can only really be fielded by mechs and vehicles, especially with reasonable speed and survivability. I like to mix critting protos with hole-punching vehicles and quadvees in the same speed bands for my Hell’s Horses formations.
Similarly, I think with the exception of one Minotaur design, protos have difficulty mounting the long-ranged ACs and HAGs for anti-air duty.