Aero bikes are faster? Why does people prefer light bikes? (the math behind)

Old debate, some likes aero bikes, some lightweight. I did the math to show, how aero is faster and why lightweight bikes feels faster.
I compare rider on two virtual bikes. The "lightweight one" is 1 kg lighter than "aero one". Weight difference comes 500 grams from wheels (rotating mass) and 500 grams from frame (non-rotating mass).
I compare two scenarios - accelerating and climbing. At these situations your work is spent to increase your energy - kinetic or potential. Riding at constant speed at constant altitude means, you do work to equalize drag and weight does not matter. But aero and other resistance losses does and that is important!
Enjoy and share your thoughts!

[slayergut]

I’m usually riding in a group around 20ppl and I’m usually hiding in the 3-4row with occasionally 1-2km climbs. I’ve tried a venge but it doesn’t really seems to be much faster on the flats maybe because I’m drafting, but I can definitely feel the difference on the climbs compared to my tarmac.

I still prefer a lightweight bike with 40mm wheels. Unless I’m doing a ITT maybe I’d go with an aero bike..

[maspurboyo]

I think that there only one diference if you like your bike you will ride it everyday everytime, but if that bike does not make u comfortable u will not ride it, eg:i was riding mtb but on the gravel road but i was riding it every single day while its raining or not, but now im grown up i have my bianchi like i dont ride it every day and it feels not as comfort as my mtb to ride

[transkryption]

I heard light bikes have faster climbs but slower descents?

[loc]

Is it worth investing in lighter wheels? Is is just that they feel faster and they aren’t actually faster?

[janeblogs]

Why do Europeans write, instead of . it's a decimal point not a decimal comma.
You even say point in the video but write comma

[jimmyhor]

Its not 2kph faster. 10 watts saved at 40kph is about 0.5kph