Note that parties are encouraged to belong to multiple coalitions, not just one. That's what makes it different.

The point is to encourage ideological unity without encouraging factionalism and faction loyalty. Factionalism under a majoritarian system induces bipolarization and correlation of behaviors, quid-pro-quos etc. all of which reduce representation by having representatives forced to fall in line.You lose independence, this is a way to restore it.

Think about it like this. Each party is a slice of the ideological space. Allocating parties proportionally creates overlaps between the slices, but this overlap is not useful in practice since parties will tend to group into opposing factions to get stuff done due to majoritarian voting. So parties will tend to create long-term correlations between themselves and deals to get votes.

This effectively splits the ideological space into two, and anyone who's ideologically between the two main factions will be represented by neither due to oppositionism. The party overlaps along that divide lose representation. This is the typical "lack of bipartisan support" scenario for things everyone wants.

With the explicit coalitions, you have each coalition being a slice of ideological space as well. Each slice has subslices for the parties.

Electing proportionally to the coalitions means you guarantee coverage of the entire ideological space. There's no single way to split it in half anymore, because any line you draw will depend of multiple coalitions, not just two big static ones formed by necessity.

So there'll be less of an incentive for representatives to fall in line because they will fall in line with the relevant coalition they're part of in a given moment.

It's the same idea of Condorcet systems. You divide space into two multiple times to find the most representative majority. Condorcet voting can find a consensus because of this.

Having parties belong to multiple coalitions is roughly the same idea as having voters favoring different candidates in a pairwise ranking in Condorcet systems.

Not having the coalitions like this is more like FPTP. You must pick a single side out of two dominant ones.