Just because they're free doesn't mean they're mostly useless. Some of the Free Servants can turn out to be very powerful and useful in almost any situation. Here are the Free Servants that can be useful.
Kintoki as a Rider still stood as one of the most powerful Quick Servants despite the presence of Merlin due to his massive Quick Boost skill, NP Boost and decent hit counts, allowing him to spam a single-target NP with great impunity.
Chloe is a great all-rounder that can boost her own performance via her Buster-Arts-Quick boost and in addition of tanking herself with a variant of Mind's Eye. And in case of single target enemies, she'll do well to eliminate them.
BB is an Arts-based support-attacker hybrid that can heal, stun, remove party member's debuff, sustain the team's NP while generating hers fast enough, remove enemy's invincibility/evade, she's overall versatile and can be used at any moment. Being the only Moon Cancer class in the game will also give her a niche that only she can provide.
Nobunaga is the first welfare Servant and she'll still provide great assistance for a long time: In between powerful Buster AOE NP and being able to increase her own critical damages, she'll be a solid attacker and also dealing extra great damage to Divine Servants, which is aplenty in the game.
David is one of the earlier 'Singularity Clear Servant' that can be extremely useful until you get your hand into a greater support. This is namely due to his party-mass evade in addition of capabilities of healing your team, making him a great support for his class and rating.
Assassin Shiki is quite decent in normal fights, but her shining quality is her capabilities to induce instant death with high success rate to almost any normal enemies. If you see a buffed up normal enemies that bar your path from challenge quests, you can simply send her in to take care of it.