Would probably need to start looking at reducing chargen skill points too.
You really don't. Current Skills "C" combat focused character (Samurai/Phys Adept) takes a Ranged skill, a Melee Skill, Sneak, Perception, and throws around some specializations. 2 Group points into a throw away group skill and done. Changes are that the character can use more weapons, which is 90% cosmetic since most runners have a weapon of choice that they'll use almost all the time. And the throw away group skill points do about 30% more. yippee.
Skills "B" for Mages, Deckers, Technomancers, changes very little because the core skills for those roles didn't change. You're still taking Sneaking, Perception, and maybe a gun skill to go along with the core required skills. Your 5 Group skill points are likely tied up in a group skill related to your Archetype. Those particular character types rarely had skill points to burn. You're still not going to trade off points in Spellcasting or Computer for the Outdoors skill.
The character concepts that benefit the most from the re-arrangement are the Mundane, non-hacker, skill monkey concepts with an A or B in skills. Those particular builds are rarely mechanically optimal. I'd be pleasantly surprised if somehow those kinds of builds could suddenly compete with Mages and Samurai. They absolutely still can't btw.
Ultimately what you've got is Riggers who can fix anything and Samurai that can use an Ares Predator and an Ingram Smartgun. oooooo, Oh, and people that can perform a standing back flip can also swim, and folks that can bring a mostly dead runner back from the brink of death to combat functional within 20 seconds can also install Cyberware and diagnose cancer. Again. ooooooo.
Skills A is still likely a Trap, just slightly less so. Plus players will be less likely to over invest in skills in the first place since there are just less skills overall that they feel the need to have.
And PiXeL01, yes. Earlier editions of Shadowrun had less skills that were broader and about the same amount of starting skill points IIRC. I don't recall any of my earlier edition characters struggling to cover "the basics" like 5th edition characters seem to.