To be very straightforward, yes, a police department would very likely have records of their past interactions with you in the form of police reports. They cannot just throw them away because it's been scrubbed from your public record. They detail the interactions the police officer had with you.
That being said, those records would not show up in a general inquiry into your record, because those records are meant to protect the officer and the department as a reference point they can go back to in case some dispute arose in the future. If a police officer really wanted to find them, they'd have to do a bit of digging for them. The difficulty in finding them would depend on what system the particular police department uses to store those records. Smaller departments may just file them in a cabinet somewhere, whereas larger ones may actually have their own searchable database. But a traffic cop out on the street is only gonna see what you're seeing at the DMV - nothing.
There is also a formal NCIC database, but traffic violations would never end up in there. That is a national database that basically stores red flag persons of interest (think stolen vehicles, sex offenders, and gang members). Sometimes multiple departments within a state will share their information with each other, but a department's database is usually kept to that department only.
Also keep in mind court records. The court case that had a violation removed under such and such conditions is still gonna be a public record. Those records would generally be available to a judge overseeing your case so if you repeatedly end up in court for the same thing, they're gonna know and they're gonna stop scrubbing it from your record or offerring certain options because you're clearly not learning your lesson. Many laws allow you to have one offense stricken per year and similar stuff like that, but that kind of stuff doesn't just permanently disappear. They have to keep record of it in order to know you've already had your once per year etc.
Also a note about parking violations: not all of those are actually issued by police. If it was issued by a private firm then that is not something that would ever show up on your record. It would just be in a database somewhere with whatever private firm issued the fine. Those kind of tickets get sent to collections and hurt your credit score if you don't pay them, rather than affecting your driving record.