Is it normal to have a laggy timeline with a great PC?

These templates you are talking about, quickly build many complicated structures to generate the desired effect.

It adds multiple layers (often 3 or more) to each transition area.

Now, you are talking about many transitions.

I can imagine how your timeline is filled with blocks that the templates need.

Using templates as transitions has a lot of disadvantages:

• Slow renders because each layer holds a minimum of 1 effect applied, often more, 
• Overcomplicated sequences
• It is hard to change the transition length
• Adjusting the effect is nearly impossible
• You must be satisfied with the effect you get, or replace the entire block with another template.
• Some templates even import video files, that may not match your sequence resolution and frame rate.

Even with a well-equipped PC, you are struggling with performance.

This is what templates do.

Try working with actual transitions (software/plugins) that work natively in Premiere Pro.

In general, they will cost a lot more than templates.

But you will benefit from the speed and versatility this will bring to your edits.

Here are some good providers of well-built fx:

BorisFX , Red Giant , Film Impact video transitions 

Premiere Gal launched an excellent video on clever video transitions that blew my mind:

Smart drag and drop transitions for Premiere Pro