Iphone users. Whenever there's a new iphone that comes out does your phone slow down and scew up?

Iphone users. Whenever there's a new iphone that comes out does your phone slow down and scew up? - 1

No…

No.
I use an iphone 6 on a daily basis.

I still have my old iphone 4 & iphone 5 which are both fully updated and both work perfectly.
(I use them occasionally for software testing).

I do always get the model with maximum storage in whatever series. I can imagine that if people buy the smallest storage ones, that quickly gets filled up then the phone starts to run out of capacity when trying to download and install updates.

That's like trying to update a PC when the hard drive is absolutely full and there's no space to download and unpack the update files, a recipe for disaster…

If you do a full backup (or two) on itunes then reset the phone completely, erasing everything, it will be like new and you should be able to install updates easily - then restore your backup.

If it's already corrupted and messing up, rather than just a factory reset do a DFU update while connected to itunes. That fully re-installs the operating system, fixing any corruption.
After finishing that you can again restore your backup.

Yes, If you install new updates. Apple planes on their phones becoming obsolete. You likely have noticed over the years that your phone that was once super fast when you first got it but became slower over time. This isn't ware and tare, computers don't work like that. As updates are released they demand more of the system resources. Eventually, they slow so much that the owner of the device will get a new one and celibate it's new lightning fast speeds. But, it will happen again in a couple years.
But to be fair, it isn't just Apple. They all do it.