This got me thinking, what are the actual roles in 5e now?
Anything you want to be, free for all.
For me a "role" playing game is a lot about distributing responsibilities according to each other's strengths and weaknesses. But I despise the idea of codified categories to conform to, especially since there are typically
many roles assigned to each PC, and so for me blanket roles just cause unneeded restrictions on the long term.
It works much better to me to see game as a "continuum" of roles blending into each other, to the point that each spell, feat, class ability or magic item can change your overall role a little bit.
If you want to.
No mandatory roles doesn't mean you cannot design a PC around one from the beginning.
How necessary is the Healer?
Not at all.
I can't claim a specific number here, but if a Healer would (for instance) provide 50% healing of HP damage and other negative conditions, very roughly this may allow the DM to stretch the "adventuring day" by 50% (actually somewhat less, since a Healer doesn't restore other used daily resources such as spell slots).
However, there is absolutely no need to stretch the adventuring day. If you like adventures with more battles in each day, then stretch it, but then why not a second Healer, and a third Healer? They all stretch the adventuring day a bit more, so they are all "necessary" for someone who wants an even longer PC party resilience.
But all in all it's just an illusion. You can lower the CR of the encounters and increase the number of encounters at the same time, achieving the same stretch without healers in the party. But at the same time, not having a Healer means having someone else with other resources to make encounters easier, so you have to see the end results to judge, rather than assuming a Healer always makes the game easier.
Is Striker a unique enough set of skills to call it a roll?
Maybe.
High-damage dealer mostly has the role of speeding up a battle towards its end. That's certainly one strategic role. There are many ways to achieve this however, and at the very least there's two main options, melee striker and ranged striker. Ambusher is also a tactical variant (based on focusing all your skills on the first strike, presumably at the expense of the average) to both.
What do you think the roles that need covering are?
None.
If you mean from the point of view of what the game books provide, it's ok to suggest blanket roles for beginners. OTOH it is too restrictive to design the whole game around them, unless you want a very specific game rather than a game with endless potential.
If you mean from the point of view of a single gaming group, you can just go back to your older edition habits and use those roles (I am sure you can do so in 5e too) if it makes you feel safe, but in general terms there is no single role that is truly irreplaceable. If the game
seems unplayable, try harder but also remember that your DM isn't irreplaceable either.
And how would your priorities them in a small group?
I wouldn't.
If you know something
before you start playing, it makes sense to make some character design choices to suit the anticipated challenges. In that case, you can agree on some priorities.
But if you don't know that, rather than worrying about 'covering' some abilities, I would worry about not 'overlapping' with other PCs. There are some abilities where overlapping doesn't have any bad side effects, but in other cases there is a risk that the better PC will always go first and fix the problem, making the second feel redundant.