Democracy is expedient collective decision making. Aggregates of people, defined spatially (i.e. by neighborhood), select a proxy to represent them in making decisions that effect all the neighborhoods in the collective we call "country".
The proxy, aka scumbag or politician, is chosen for various reasons by various people. Many people do not bother to vote, being happy with the status quo or realizing that their vote is not significant (the weight is typically 1/N, where N is a big number - even if most don't vote) and thus not worth the effort. Everyone casts their vote, the votes are counted, and some rule is applied to select the winner(s). We now have a set of proxies to decide for us - most of whom we never heard of prior to their political life, who we never see or talk too, who often have not lived in a community or have anysort of meaningful relationship with that community, who "lead" a "community" that is most often hetrogenious and mobile, have not grounded themselves with serious considerations of social, historical, and economic facts and ideas, etc. So very imperfect proxies, but those are the proxies we have.
What are the bounds on these proxies? There are a few - social norms and the media are two important ones. Parties are another important one - most politicians align themselves with a party in order to signal what they stand for. This party affiliation bounds the behaviour of a politician, mainly through the power relationship of the party (which will punish them for failing to follow the broad sweeps, as well as nitty gritties) but also through "optics" - breaking social norms, such as "flip flopping" on key principles and platforms of ones party, is also punishable by voters, by politicians peer groups, by becoming a legitimate target for mocking in the media, etc.
So the situation is this: we have a group of M contenders viaing for N (N lessthan M) highly valuable political positions, these contenders group themselves in parties, and after posturing voters select N to fill the positions. Then N consists of various factions, which are bound by the parties they are in, which must posture and fight and showboat their way forward, making (mostly costly) decisions of various sorts. We all pretend that they have our interests at heart, and hope we don't get too screwed.
So - given that negotiation must occur to decide various outcomes, does it matter is politicians switch parties post elections. i.e. form a set in coalition. After all, the politicians are aligned with a party, the party makeup is now set, and is various parties coallesce together does this make any functional difference?
The answer must be yes - otherwise the parties would not bother to coallesce.
In addition to this observation, we must also confront the fact that we are not averaging together parties in order to come up with a new party that accuretly reflects those parties. Instead we are averaging together members of parties, who are only partially constrained and defined by the party. Those members will define the new party in their best interest, yes constrained by "optics", but since the ruler is living by party platform and most voters are partially (to not at all) informed there is ample wiggle room.
I previously argued that perception of legitimacy would be seriously harmed, and this is one key problem with allowing ex post redefinition of parties: in business changing a product after a contract was negotiated is fraud, and I don't see how this is any different here. Some will say, but this is inconsequential - its like you require a car, and negotiated red, but you got the exact same car but it was blue. Is that really "fraud"  But I think things go even further, and there are actual choice consequences - the path society will travel changes. As noted above, the parties joining a coalitions definitely believe so - otherwise they would not do so.
It is hard to come up with a clear example the demonstrates this - the fact that coalition is being considered at all demonstrates that the politicians believe there is a difference in outcomes. The fact that people support this based on "expediency" suggests that deep down they do also - after all, if there is no difference in practice it is just as expedient to simply ban set coalitions and you loose nothing - as nothing would have been gained from allowing it. This demonstrates a belief. But in a vague complex system it is hard to come up with a nice clean demonstration of this.
So as of now, I have the following:
- coalitions are fraud: to some this fraud is so inconsequential that it doesn't matter, though to others with different preferences it may be huge - thus basic legitimacy is called into question, and this may have very negative implications for society
- both coalition members to be, and people in general who argue pro-coalitions, implicitly believe there is a functional difference: otherwise there is no point in doing so, in particular there is no positive to overweight the (possibly small, but possible large) legitimacy issue.
The hardest part - coming up with a clean example - will have to wait for some sort of inspiration....
 Yes. What people think is important and their preferences are often vastly different, and we can't predict or sense how important things are to others, unless we really know them well. For some the colour is completely unimportant, for others that may have been a key selling feature. For me the expediency argument of allowing coalitions - we must make decisions and it is a waste to go back to the polls! - is an implicit statement that others preferences are not important. To me red/blue is stupid, and it is "expedient" to move on - the basic car features and where we are going define expediency, but to someone else perhaps the red is key - they reconize that all cars are basically the same, and pick based on colour as this will make the trip more pleasant, or allows them to feel good about investing in the upkeep of the car, is the truely important distinction between their top two choices, etc. They may not be fine with averaging together red and orange, even though the colours are "very similiar" and are "quite different" than blue.