Yeah, that makes complete sense, it's probably something that would be good to remember when we eventually play it to not overdo it with penalties that come from me (as opposed to those the system dictates) It's actually kind of interesting because the game frames 2 dots as professional, but it's out of 5 dots, so it's still in the bottom half.
Looking over it, the main saving grace to avoid that is actually willpower I think, you get Resolve + Composure, and recharge one spent one every night of sleep, and it applies a 3 die bonus to the roll, and you can further recharge it via the anchors. But I can certainly imagine it running out or players trying to hoard it for 'important' rolls, or even skimping out on those two attributes and not having more than the default of two willpower.
But if you can use willpower, your 3 die pool (already after the penalty you applied in your example) pops straight up to 6 dice, which is a lot better. Honestly I did not realize willpower was this powerful in the system, in a lot of situations like the ones you're talking about it'll straight double your dice pool, when I'd seen reference to it my brain had actually pegged it as being one additional die.