Computer Glasses Prescription

Is there a reason my eye doctor would give me weaker prescription eyeglasses and stronger prescription computer glasses? Affordability is key here as my progressives already cost $600 (frames not included in that price) and computer glasses would be another $300 on top of that. Why can't I get a stronger prescription for daily wear? Yes, I understand the span of computer protective glasses compared to daily wear.

Right now I am struggling to even focus when I use the computer even with the font size changed and it's causing terrible strain on my eyes because my eye doctor prescribed weaker daily wear and I feel like I'm being forced to buy computer glasses. It took 3 weeks to get my lenses and I'm not sure I can take these headaches for another 3-4 weeks.

Also - wouldn't the wear and tear of taking glasses off, and putting the others on all day long, be a setup for the frames to potentially break faster?