Banishment requires a specific material component:

an item distasteful to the target

So does summon greater demon (XGtE, p. 166):

a vial of blood from a humanoid killed within the past 24 hours

I thought I had seen this question here before, but I couldn't find it to double-check, so I'm asking again.

Are these components with unique attributes assumed to have a cost? Or can they be replaced by a component pouch or arcane focus?

My interpretation is that cost isn't just gold - it is any sort of condition on the item (so, distasteful items or blood with timer requirements have a cost). Therefore, both these spells would require specific components to be cast. Is my interpretation correct?

RAW only things with a Gold Value are costs

The spellcasting rules on components state:

A character can use a component pouch or a spellcasting focus in place of the components specified for a spell. But if a cost is indicated for a component, a character must have that specific component before he or she can cast the spell.

You cannot replace material components that have a listed cost however.

What is an indicated cost?

By RAW a cost is only for components with a gold value. For example, Identify has the unique costs:

A pearl worth at least 100 gp and an owl feather

In this case the owl feather can be replaced by the focus or component pouch. While the pearl cannot as it has a gold value cost.

How does the component pouch/spell casting focus replace the components?

The spellcasting focus does exactly what it says, it provides a focus for the caster to channel their magic through. The assumption is that without their focus they need much more complicated components that have some relation to what they are trying to do. See What is the point of inexpensive material components? for relevant information.

Could a unique requirement be considered a cost?

Certainly, if your DM rules it that way. However this is not RAW and we don't have enough information to know if it is RAI.

What would happen if it was ruled this way?

Your casters would have to work a lot harder for their magic. This isn't necessarily a bad thing. The number of spells with these unique requirements isn't that many. This could be a great opportunity for roleplay in obtaining the acquisition of them.

At then end of the day the answer is "Up to your DM" as with most rules based questions.

How would I rule it?

For requirements that could be fulfilled by any number of items, I would allow the focus to replace it. This covers your first example. As there are hundreds of things a creature may find distasteful.

For time limited requirements, I would rule they cannot be replaced. As you point out they are unique constraints and particularly the one you quote could raise questions as to how it was obtained.

Cost refers to money

The rules on material components state:

Casting some spells requires particular objects, specified in parentheses in the component entry. A character can use a component pouch or a spellcasting focus (found in “Equipment”) in place of the components specified for a spell. But if a cost is indicated for a component, a character must have that specific component before he or she can cast the spell.

There are three aspects to this:

1. Cost must be specified. Being distasteful is a property; it is in no way specified as a cost.


2. All material components are described in a "mystical" way, with a sense of being hard to get. Where would you draw the line? If a line was intended, it would be in the rules.


3. 
   

   Cost is not defined in the rules, so the common definition applies. Using Cambridge Dictionary, we see that cost is:

   
   
   

   
   

   the amount of money needed for a business or to do a particular job

   
   

   
   

Thus, if something isn't specified in cp, sp, gp, pp or similar in-game money, it is not cost.

According to this Sage Advice talk, it is pretty much up to the DM. At the same time, this discussion sets a gp worth on components with no listed cost in the spell itself, so I'm not sure if it should be considered, given it contradicts RAW of the spell...

As always, if it makes for a good story, ask your DM. If it would be an obstacle for your players, warn them.