I'm betting that your Pioneer wasn't cheap. Within the market for all-in-one systems, Pioneer was a cut above the rest. The system design looks like it dates from the early to mid 2000's when DVD was still a hot commodity and when Pioneer was king of the hill in TV sets.
The point is it was designed with a certain set of goals in mind: Small size for the head unit and speakers to be domestically acceptable, integrated DVD, MP3 playback, a big wattage figure. All of these things designed to appeal to a certain type of buyer who might not know about separates AV gear, or if they did then it wouldn't be acceptable on size grounds. So, it's not about price but more about design intent.
As you've correctly pointed out, today's all-in-one systems continue the trend of leading with trending features - Bluetooth, wireless subs, App features etc, and this is done at the expense of audio quality and flexibility which are seen as lower priorities for the target market. Separates - even the entry-level gear - are built with a greater focus on sound performance. It's a different set of design criteria rather than the absolute of price that makes the bigger difference.
The bottom line is that whichever powered sub you go for, it's likely to be an upgrade from the Pioneer one. The reasons are simple: 8" or 10" driver vs 6" for the Pioneer. . Built-in power supply matched to the driver. Better built and more rigid speaker cabinet. Greater bass extension. Precision controls for volume, phase and crossover point.