Undoubtedly, but the balance of cash paid in subsidy versus the additional infrastructure costs of not having subsidised buses needs to be part of the bigger picture.
However, in practice, that never happens. When looking at subsidising buses, authorities aren't thinking of the cost of building a new road vs the alternative. When a new road is considered, the cost benefit analysis simply doesn't look at the impact of improving local bus and rail services in any meaningful way.
We do seem to going off at tangents in this discussion though...
Perhaps the cap should have been increased in smaller increments - 50p now and another 50p later. However, we'd still have people wailing about a "massive" 25% increase to begin with; in 6 months time (or whenever the cap was planned to rise again) you'd have the same people crying about a "massive" 20% increase.
What did you pay for a single before the original £2 cap, and does the new £3 cap still provide you with a saving on the actual, uncapped, fare?
I'll no doubt get shouted down, but this isn't a fares hike; it's a reduction in the discount you've been receiving.
Back on topic, this is the nub of the issue. If you look at things in terms of percentages, any increase was going to look disproportionately severe given the unsustainably low level of the £2 fare and your point
is well founded. One example that the government picked out is Newcastle to Middlesbrough - Jan 2025 fare increases by 50% from £2 to £3. However, compare Dec 2022 (£8) to Jan 2025 and that's a 266% less.
If I look at my niece's journeys, if she wanted to go to work nearby, her fare is £1.70 each way so the cap is neither here nor there. If she wanted to go to Darlington (as she used to work there), her fare would have "rocketed"

from £2 single £4 per day to £3 single £6 per day.... which is still less than the £5 single or £7.70 day that she would otherwise incur. Of course, were she still working in Darlington 5 days/wk, her weekly ticket would be £24.70 or less than a fiver a day.
The upshot is that 50% is a soundbite statistic. Like all such soundbites, it needs context!