It goes back to the early days and "Google Scout", when the guys still believed links would invariably be on-topic and so "related" :-)
That is a false argument in which a too high standard is applied. 100% ontopic and 100% related is neither the goal nor a requirement for using links in an algorithm. After all, if it was, a link from a car store to a car stereo store would not meet the 100% requirement, and that sound prtty bloody useful a link to me!
Links STILL, even with ten gadzillion SEO sites, offer invaluable information vital to the most practically effective algorithms (as oppossed to the mythically effective like having people review every page ever second). Noise, rather than a deal breaker, is simply a problem to be factored in.
It was also before there was AdSense, AdWords, and Universal Search which requires them to know the theme/category of a web site
No, it doesn't. AdSense and AdWords don't require a category at all, and Universal Search only requires that a site be tagged as belonging to a specific subset of sites, just like video, blog, linux, government, many of which have been around for donkey's. That there is a blog search DOES NOT mean that categories are used, needed or even preferable in other areas (like say cars), and especially not that "theming" is in use.
(and before link spamming became such a problem).
Is it a problem? And if so, as "before" implies a start date, when did the problem start? Making a statement like that is mioving to fast, You need to quantify it. besides, ranking websites is really just one big problem, with hundreds of sub-problems, of which link spam is just one minor issue. Saying somethign is a problem then is either a truism (i.e. trivially true) or a statement that something is harmful without evidence.
A good question is how much of an impact, if any, does it have on rankings?
Does what have? Hehehe.
At this point I can't make a determination, but I'm not ignoring it either. Why? Because based on groupings by geographic location my domains render dramatically different results when searching at the different locations and I want to determine how deep the rabbit hole goes and it's impact on rankings. I could be wasting my time and it wouldn't be the first time.
I am going to say something controversial here: nothing that any SE has done has changed SEO one bit since about 1997. Nothing. The game always was and always will be:
1. Build a Search Friendly site with consistent URLs.
2. Write naturally using words people use when talking about the thing you are writing about (aka stop speaking Marketingspeak).
3. Get links to your site from others.
That is the sum total of the game. Sure, there are lots of ways to maximise SEO, but the above is what it all boils down to, and if you take the long term SEO view, you will already be doing most of what is required to get the best results. I say that because The SEs are trying to get the best sits to rank the best, so if you aim to be the best, you are what they want to promote.
It is kinda like trying to become the right person for a lover. You either are right for someone or you ain't, and while faking it can get you quite far for a while, ultimately the truth wins out.