In PHB, page 190, it explains about the free item interaction:
You can also interact with one object or feature of the environment for free, during either your move or your action. For example, you could open a door during your move as you stride toward a foe, or you could draw your weapon as part of the same action you use to attack.
At the top of the list of "Interacting with Objects Around You" it lists:
draw or sheathe a sword
It is generally understood (reading the various answers on this site) that if you want to switch weapon and attack on the same turn (let's say you are a fighter with a sword, bow and the Extra Attack class feature; you kill the enemy in front of you with your sword, then want to switch to your bow and shoot another enemy that you otherwise can't reach this turn) then you have to do this strange sequence of moves where you "drop" your sword so that you don't waste that precious free item interaction that you need to draw your bow. Then you have to pick it up again later (assuming someone else, friend or foe, doesn't do so before you).
Basically I think this sequence is a bit daft and think that it breaks the suspension of disbelief when the fighter suddenly drops his main weapon just so that he can use his bow this turn. I was thinking of just houseruling that you can draw and sheath a weapon as one item interaction, let's call it the "switch weapon" item interaction as opposed to the "draw weapon" and "sheathe weapon" item interactions (I'm just making up these terms to emphasise my houserule).
Now, I know that one gameplay-related concern might be the Dual Wielder feat, since they can draw and sheathe two weapons at once; as so not to weaken this feat, I'd still say that you need that feat to draw or sheathe two weapons at once, regardless of drawing and sheathing. So let's say this fighter actually has two swords drawn at the start of that scenario, I would houserule that it's only possible to sheathe one of those swords without the feat, similarly for sheathing the bow and drawing the swords again later; you'd only be able to draw one sword at a time without the feat, regardless of whether you are sheathing something or not.
So hopefully that still makes that aspect of the Dual Wielder feat useful, despite my houserule. So my question, finally, is what are the impacts of my houserule on combat tactics? Obviously this question isn't asking for approval to use this houserule or anything like that, since anyone can houserule whatever they like; this question is just about understanding the impacts of doing so with this particular houserule.
The answers below question my assertion that dropping a weapon doesn't make sense. On reflection, I agree with them and not my past-self. It's not dropping a weapon that's "daft", it's my lack of imagination for not being able to see why that would make sense and why it can create a more interesting battle. This is largely due to expecting everybody to do the "video game weapon switch", which I believe is actually the problem here. I need to unlearn video games' lesson that everyone can juggle weapons and re-learn that notion that IRL that's a bit more difficult and time consuming. And if ever someone can imagine a way that a certain character would totally be able to juggle weapons around, it can always be a homebrew feat, which is much better for balance than a houserule that lets everyone do this for free. Thanks to all who answered.