The big pro is that the time works for you both to go. If you want to both go and walk the full
Camino Frances, that's your only option. In that sense it's not really a pro; its a choice, go or not.
From what you say, you should just go.
The rest is is just 'What will it be like, and how do i work around the negatives.
hot: wear a hat, lots of sunscreen, lots of water, adjust your schedule to get up earlier to walk when it is less hot (which you will learn after a day or two of walking in the heat anyway).
Possibility to bring a sleeping bag liner instead of a sleeping bag and save space/weight, which might be offset by the increased water carrying. Carrying less bulky clothes.
Busy: you will meet lots of people on the road, and you should probably book some accommodation, at least in key places like the start in Roncesvalles and the end stages from Sarria. Not confined to July, this applies to possibly half the year. you will still find ways to be as alone as you need to be in the midst of people.
It will be less green and more brown than earlier in the year (except possibly in Galicia if they have a lot of rain). So what?