IMO Jobcenter+ lost a lot of it's commercial links about 10-12 years ago when they brought in all that hostile environment crap. You ended up with claimants being pushed to apply to 30..40...50....60...80..100 ect... jobs a week and provide evidence of it. So pretty quick claimants start to run out of appropriate local jobs to apply for and end up having to apply for any old stuff, including jobs they have no realistic chance of getting. The result is employers getting swamped with absolute dross time wasting applications, how many lackluster interviews must have ended with "And what attracts you to this role?"...."Nothing, The jobcentre made me apply". Employers will have got sick of that level of quality pretty fast.
Their Universal Jobmatch service didn't help...rapidly became a total mess of spam and fraud due to hands off moderation, one of the final straws was the DWP insisting they had no responsibility for anything that happened on the service, at all...so you have a situation where claimants are contractually obligated to hand over their personal info to known scammers by the DWP...who claim to have no responsibility for the consequences...fail. That didn't do much for employer links anyway. the service was quietly killed after a few years despite being a flagship launch.
10-15 years ago they essentially liked to outsource the jobseeking/skills bit to semi private companies with varying results. But he trouble was most of these places were only viable with extra funding help/grants from government and councils, so in the 10 years of public cuts most of these things have wrapped up one way or another without much to take their place, this is when they tried their phase of 'So how would you like you work for free?' jobseeking, which went down about as well as you'd expect.