On-page SEO isn't much work and it has the least effect. You just have to adjust your header, meta-description, general tags and make sure that your site isn't taking much time to load. That's it.

Where is the article of which you speak? I need to see this article!

Yes, Website having only strong on-page SEO is able to rank higher in Google search results.

Yes, On page seo is the most important part of seo, without on page seo u can't get organic traffic, so first do On page the Off page

on page SEO works if you do proper meta description,tags etc.
On page SEO still effective

On page SEO works. If your not concentrate on this the raking will be affected.

How SEO Works...

Although the Search Engines are continuously refining how they rank web pages, there remain two key elements that are the foundation for successful Page 1 result...

Onsite - your content and website infrastructure

targeting the best keyword clusters

matching existing content to target specific keyword clusters

creating new content to target specific keyword clusters

having the best website infrastructure and architecture

Offsite - how your website is referred to from other online sources

developing a profile of high quality, on-theme incoming links

having a relevant and active social media presence

creating citations (non-linking references) about you

at least half of your SEO outcomes are influenced by elements outside your direct control

...and everything else is about strategy, techniques, tactics and finesse - the Search Engines look at over 200 "signals" when evaluating web pages, and every year they add over 400 refinements - so a key part of our job is keeping your website at the leading edge...because we do really know how SEO works

On Page SEO really works on SERPs because it directly impact your website.