Since you're earning a living off it, a conservative approach makes sense for sure.
First a few thoughts...
They say it would be too difficult to split the site
There are a couple of considerations here. If you want Wordpress to run two sections of the site, but not the home page, you do have some challenges you don't have currently with WP running one section.
The main problem is that if you try to run something other than Wordpress for your homepage, the you pretty much have to put WP in a subdirectory or subdomain (effectively the same thing in most CPanel setups). So if you want two sections running under WP, you'll need to either
- Wordpress (or whatever CMS) runs the front page and various sections, but does not run other sections. This is the option that makes the most sense to me.
- Static front page and you run two installs of WP - one for each WP section.
- One section with WP and the other sectino depends on some sort of rewrites (not 301 redirects, but rewrites), but that won't come through in your WP navigation
- symlinks to share a WP code base, but again I don't think your navigation would work
In other words, at the point that you want two sections to be run by WP, IMO the simplest solution is to also turn over the front page to WP. Then you just add the necessary Rewrite Conditions so that WP doesn't take over the parts you want to keep outside of WP.
That said, you do have a maintenance hassle with two sets of navigation - WP and your static site.
As for your concerns:
>> my page addresses would change
Why would your URLs change? That shouldn't happen.
>> unnecessary code will appear on pages
True. To some extent, though, having the same CSS and JS load on each page helps with caching on subsequent page loads. So it depends a little on how big that initial payload is.
>>risk of attack
True... but you already have WP on your site, just not on your front page. It seems like overwhelmingly, you're taking that risk already. Your added risk is primarily in the plugins I guess.
>> cost of constant upgrades
You already have WP running on your site. How does having WP run more of the site increase your cost of upgrades?
>> loss of design control
What design control do you lose? Do you mean designs that WP can't implement or designs that you personally can't implement because you don't know WP theming that well? In other words, is this a worry about design or about design costs? I would tend to discount the former, but the latter could be a serious consideration.
None of this answers your question... my personal feeling is that I dislike dealing with hybrid sites in general, but except for my very first experiments in 1996, I've never had a static site. So for me it's been a question of a custom DB-driven site versus an off-the-shelf CMS and usually I think if someone else has already done so much of the work, why would I try to program it myself. But that's a different question.