I agree with you that the components as they appear are flavour and not substance, and it's asy for a campaign to do away with them.
I would suggest, however, that if you are going to try to take away the focus from casters, that you let spills still be cast without it, only the caster cannot add their proficiency bonus to the DC. The spells are "unfocused", but still castable. (That's actually the way I thought Material components should have worked from the start.)
I understand why you would recommend this, but I don't think it is overly harsh to say that they must have either the component or the focus to cast the spell. The material component is actually a focus, a way to help you get in touch with and manipulate the weave of magic. An arcane focus, druidic focus, bard instrument, or holy symbol allows you to take that deep understanding of the magical nature of the material component and focus it through this spellcasting focus. It is a shortcut only available to dedicated spellcasters who have spent much time deep in study and practice.
In short. If you have a spell-casting focus (and are of a class that has spellcasting focus as a class ability), you can cast the spell.
If you do not have a spell-casting focus, you can use the actual material component.
My only change is: in order for your spellcasting focus to replace a material component for casting purposes, you must first have studied and practices the spell with access to the appropriate material component.
That doesn't, IMO, nerf casters. They can hide multiple component pouches on their person if they are worried about losing both their focus and components. They may also want to have some safe house, store room, hidden cache, or laboratory where they store extra components in case they lose the components on their person. This just drips spell casting flavor for me.
One other change I am thinking about now is that the spell caster can only be attuned to one focus at a time. But it is a special focus-attunement slot that doesn't count against magic item attunement limits. Otherwise, at higher levels, the caster can just have, say, an extra wand hidden on his person. I like the idea that if your wand/instrument/staff/holy symbol is broken, stolen, lost, you need to get somewhere where you can take the time and money to make or buy a new one.
On the other hand, allowing multiple foci can lead to some fun roleplaying.
DM: "You wake up in a dark cell, stripped of all your possessions and clothes."
WIZARD: I take out my wand and cast light.
DM: You are naked. All your possessions were taken from you. Including your wand.
WIZARD: I had an extra one hidden.
DM: Where would you hide it‽
WIZARD: ... Do you want me to draw a picture?
DM: Ugh. Yeah, right, you've been walking around the dungeon with a stick up your ass.
FIGHTER: It would explain a lot.
WIZARD: Look, it is written on my character sheet. Both in the equipment section and my character's background. Fecesious Stercus went to an all-boys wizards academy and to get around forgetting or being able to procure needed components to complete tests, they would sneak--
DM: OKAY! Fine.
WIZARD: Oh, I also have components for
banishment and
true seeing.
DM: *Sigh* Fine--What? True seeing‽