That is a very good question and actually my current research topic. I try to give an adequate but concise answer¹.
I will focus my answers to networks based on the IEEE 802.15.4 standard (Zigbee and 6LoWPAN both use it as physical and data link layer) as well as networks where most traffic goes through a common gateway. Most arguments also hold for peer-to-peer networks, but it is more difficult to define what a network is (e.g. if your neighbor and you both use Zigbee devices).
¹ I will hopefully be able to fill a whole PhD thesis by answering the question ;-)
Is there something about mesh networking that makes it inherently limiting in terms of network size?
There are several factors that limit scalability in wireless mesh networks:
- There is only a given amount of traffic that can be handled by a single node and this especially holds for the gateway. Thus, in general, if you double the number of nodes, every device can at most transmit half of the number of packets per time.
- With more nodes in a mesh network, there is more chance for complex arrangements that generate many problems in the routing layer and the link layer. One example is the hidden node problem that increases the probability of overlapping (and therefore failed) transmissions.
- The more hops a packet has to take to its destination, the higher is the probability that it is lost. Much simplified: If the probability is 99% that a packet transmission fails, the probability is 0.99^h for h hops.
- More nodes are more difficult to maintain. For example, updating the software manually is OK for 10 devices, but not for 1,000. So you need some kind of remote software management.
So there is no inherent limit to the network size itself (apart from maybe your address space...), but a reliable communication gets increasingly complex and error-prone. Of course, deploying a network with thousands of nodes should be possible if every node only sends one message per day. But a network of 1,000 nodes where every node sends many messages per second will overload the channel.
That said, this does not make wireless mesh networks per se worse than any other wireless technology. Cellular networks can only serve thousands of devices because the providers own a large amount of the wireless spectrum, they clutter the area with basestations and only few devices want to communicate at the same time². And the LoRa technologies certainly have their applications, but in the claimed highly scalable networks the throughput is far from what a IEEE 802.15.4 mesh network can deliver.
And to address your comment: No, overall distance is not the actual problem. In fact, the main advantage of mesh networks is that a larger distance can be bridged without increasing the power or reducing the data rate.
² I do not want to say that cellular networks are bad, but just that you can not compare the scalability of a city-scale cellular deployment with a wireless mesh network with a single gateway. (And multiple gateways are possible.)
Are wireless mesh networks limited to PAN applications?
The definition of the term PAN is quite fuzzy, depending on the context. If the only distinction is a low number of nodes, the answer is already given by the previous part. However, as the name indicates, it can also mean "a network for interconnecting devices centered on an individual person's workspace (Wikipedia)". So this question has another dimension, that is if wireless mesh networks (according to IEEE 802.15.4) are limited to personal applications.
Are industrial wireless mesh networks feasible?
I was contributing to a research project that assessed the feasibility of a wireless mesh network in the context of a solar tower power plant. And as far as I can say, using a wireless mesh network in this application is very promising. While we did not had the opportunity to deploy a very large network, there are other very promising industrial deployments, for example
T O’donovan, J Brown, F Büsching, A Cardoso, J Cecı́lio, J D Ó, P Furtado, P Gil, A Jugel, W-B Pöttner, et al., The GINSENG System for Wireless Monitoring and Control: Design and Deployment Experiences. ACM Trans. Sen. Netw. 10(1), 4:1–4:40 (2013).
There are many reasons for using wireless technology, but you only need wireless when movement is involved. This is especially the case for all kinds of vehicles. Furthermore, there is a current trend to replace cable carriers by using wireless technology, but that is only a point to point connection, no need for mesh.
A second argument can be a cost consideration: The deployment of cables can be quite cost intensive, especially outdoors, so for example in solar tower power plants wireless devices would actually reduce the investment costs (maybe a lot) even if it is not required because no mobility is involved. That might or might not be applicable to other industrial applications. Clearly, choosing the right number of basestations and thus the size and performance of a single mesh network is a trade-off that involves cost considerations, too.
So, why are there so few industrial wireless mesh deployments?
Short answer: Because cables are great and well-proven!
At first, finding applications where wireless technology really shines is not that obvious (see last section). Then there is the energy aspect: There are applications where energy harvesting work very well (including solar tower power plants), but otherwise you have to rely on batteries (that might induce high maintenance costs) or power cables. Cables only for power might actually also be beneficial, for example when retrofitting old factories that provide power everywhere, but there is no space for additional data cables.
Certainly, in the future there will be much more industrial wireless applications and also wireless mesh networks will find their niches, but it is obvious that new technologies find their application first in personal environments instead of industrial environments where problems will have much larger consequences.
EDIT: I just noticed that the IEEE changed the title of the IEEE 802.15.4 standard from IEEE Standard for Low-Rate Wireless Personal Area Networks (WPANs) to IEEE Standard for Low-Rate Wireless Networks according to this correction sheet published last year. The reason for this was probably that "personal" does not really fit to the standard anymore as I argued above.