Personally, I don't value extra spell slots that highly, most single casters aren't going to be burning through 2-3 spell slots an encounter to reach the point where having 20+ spells is worthwhile.
With 6-8 encounters per day, having 3-4 rounds of casting plus some bonus actions and reaction spells (thank you shieeld, counterspell, etc.) is completely reasonable. Lowballing 6 encounters of 3 actions plus a single reaction/bonus action spell is 24 spells/day right there. Not including any utility spells cast at other times.
That pace is probably common for an entire adventuring career. Let's look at the balance as we go up the levels.
It starts at 2nd level, where you have 4 1st level spells instead of 3 - a 33% increase, and easy to use in an adventuring day. But that's just a scary percentage, not really a big deal. Though if you offer a 2nd level caster a free 1st level slot, I think it's a safe bet they would be happy taking it.
At 5th level, a single classed caster has 9 slots vs. a dual-classed caster/caster will have 12 slots. Both are 16 spell levels worth. Okay, that's not so bad either, if there's a imbalance it's probably in two subclasses coming on line vs. the 5th level caster feature, but that's a different discussion.
At 8th, single classed finally gets up to those 12 slots and 27 spell levels, but dual is up to 18 slots and 32 spell levels. That is a big deal.
At 11th single has 16 slots vs. 22 spell slots. But it's caught up in spell levels, with 47 vs. 46.
At 14th single has 17 slots of 54 spell levels, vs. 28 slots and 72 spell levels. It's here that we're finally getting to the point where there might be "too many" spell slots to use all of them effectively for the dual casters based on the combat math at the beginning, so we'll see more utility and other out-of-combat usage.
For completeness, 17th is 19 slots and 71 spell levels vs. 32 slots and 94 spell levels. 20th we already discussed at 22 / 89 vs. 34 slots and 108 spell levels.
Consistently the dual classed casters have an edge in slots, and for most of the time they also have a considerable edge in the total spell levels of those slots. It's not until the last tier of play is there consideration that they may have "too many" slots.
And lastly, many lower level non-damage spells keep their utility and scale well without needing to e upcast, so having more of those slots is useful. The single classed caster can use more of those by upcasting (for the spells that allow it) or just using a higher level slot for no benefit, but that makes the castable-spell-levels even worse in it's favor.