We've had application-specific integrated circuits (ASICs) and systems-on-a-chip (SoCs) in this industry for a long time. But what each of those actually is has changed over the years, due to time, technology, and trends. Like so many other things, ASIC and SoC became "buzzwords," which meant just about whatever you wanted them to mean to fit your storyline.
How so? Very often, the ASIC was somewhat "application-specific," but it was often also usable in a fairly broad range of associated applications. As for the SoC, it seemed to be more a case of definition and frame of reference than actual use, since one person's "system" is another person's "component." Note that for a circuit designer, a component is an IC, a resistor, capacitor, diode, etc.; for the audio-studio designer, it's a rack-mounted chassis. So we go from one end of the spectrum to the other.
In the past years, though, there's been an increased focus in the ASIC and SoC arenas, even if those terms are not used as much. We're seeing ICs and associated software and tools which truly target well-defined applications, and aren't a fit for much else. These products integrate the features and functions that the vendors have decided are "just right" for the intended use, without extra bells and whistles. In general, there are no unused input channels for expansion, no extra memory (or memory I/O), few or no temperature-range options, and limited packaging options (if any). The end result is a targeted part at a relatively low price, because it comes in only a few versions.
For example, look at the ADS1298 from Texas Instruments, a 24-bit, 3-channel analog front end (AFE) for biopotential measurement applications. By its channel count, conversion rate, and resolution, as well as other attributes, it is a good fit for electrocardiogram (ECG) units, Holter monitors and wireless patient monitoring equipment, and a poor fit for almost any other application (this doesn't mean that clever engineers aren't already thinking how they might leverage the part for unrelated uses).
Or look at Maxim's 78M6610+PSU/78M6610+LMU single-phase energy-measurement subsystems, each in a single IC. The PSU (power-supply unit) is for datacenters, servers, and telecom and data equipment. The LMU (load-monitoring unit) is for end-use appliances, smart plugs, EV chargers, and solar inverters. Each of these does almost the whole task (separate sensor required, of course). If you're doing a power/energy measurement design, you'd be foolish not to at least consider these.
The increase in what I'll call true ASICs (should we call them TASICs?) is probably good for designers, because it gives them a quicker, cleaner way to get their own product released -- and that's an ever-more vital attribute. They also allow the project team for focus on where they bring value, usually (and sometimes only) through their own application software, especially for the user interface, as well as overall product packaging.
Note that these newer, highly integrated ICs are not a sure-thing win for the vendor. Yes, everyone wants a high-volume product, of course, but there are two ways to get it: via a few major users, or many smaller ones. Some of these ICs, such as the two examples above, have lots of potential users, while others -- such as those for automotive applications -- have far fewer. So you can win big or lose big.
Whether the growth in highly integrated ICs is good for IC vendors, only time and markets will tell. Their impact in the role and function of the design engineer is also unclear. As they change the designer's responsibility, will they improve their overall engineering skills, diminish them, or maybe both?