Specialization is the way to higher pay
It has always been this way. If you're one of only 10 people in the country qualified to a particularly narrow IT field, you can pull down $300-$500/hr as a contractor. I know a couple guys like this.
The risk is, if things change and that specialization is no longer relevant, your pay can quickly drop to zero. What's the difference between someone who specialized in a niche for SAP back in the 90s, versus a guy who specialized in a similar niche for Baan? One is still making bank, the other is probably struggling if he hasn't moved on.
Being a generalist is fine, but you need to have at least one niche you can point to as a specialty. If you want to do project management or architecture you can start in that specialty, and your generalist skills will allow you to break you to managing the whole project or as a chief architect, where someone who is truly just a specialist will not. I'm a true generalist with a couple specialties, and I parlayed that into architecture roles in that specialty and then to chief architect roles where my generalist knowledge has been invaluable. Someone who worried only about their specialty wouldn't have a prayer of success doing what I do.
The other way to go is to get hired on by a small company as "their IT guy", or contract to several even smaller companies as "their IT guy". If you're fine with doing the grunt work like running cable or installing a new PC, your generalist skills will come in handy and you can maybe sell them on the idea of giving you a bonus based on a the percentage of the reduction in "added cost" IT expenses they avoid because you can do everything (i.e. not having to have some company run cable, another company configure your new firewall device, another company migrate your storage when you buy a new RAID)