Holy crap... where to start...
[1] A 'solid axle' (not axel) has nothing to do with having a differential or not. 'Solid axle' refers to a type of dependent suspension design, also called a beam axle. Aside from that I would be stunned if you could cite a name-brand vehicle built in the last 50 years that didn't have a differential.
[2] Brake assisted 'virtual limited slip' drives have only become common-place somewhat recently. Various mechanical limited slip differentials are still quite common, as are different traction control schemes. But please, by all means, tell us neophytes how cars work, we clearly what we "think" is wrong.
[3] *affect, not effect
[4] This is a REALLY bold statement to make, especially when it comes to replacing odd numbers of tires. One should consult their owners manual for guidance. TR has a great article on this:
https://www.tirerack.com/tires/tiretech/techpage.jsp?techid=18 which notes several manufacturer specs that vary widely. Mis-matching tire sizes wrong enough can cause ABS and stability control issues, transmission mis-shifts, differential overheating and wear, excessive driveshaft joint wear, and other issues.
[5] You shouldn't be proud of the safety risks your creating for other drivers, nor should you be proud of getting away with poor practices. Apparent lack of damage or consequences in one case is not evidence of acceptable practices or good decision-making.
[6] Please, no one take this person's word.