None, really. Well, it depends what you're asking precisely. In order to explain, let me share an analogy that I've been thinking about, as a way to describe containers:

When you launch processes on Linux, you can choose for all the processes to share memory with each other (in which case we call them threads), or the processes can have separate memory. We call this capability "virtual memory", and it allows processes to pretend that they and the kernel are the only software running on the physical machine. (For example, every process might think that it can write to the memory address 0x08048000, but in fact that address is virtualized and mapped by the kernel to some different physical memory address.)

Though we take it for granted, this memory isolation between processes was the first form of kernel namespace. Modern Linux now has many of these namespaces, which can provide a virtualized view of the file system, network, IPC, uids, and so on. "Containers", then, are processes that employ many of these namespaces to provide isolation from others on the system. (To extend the analogy: just like regular processes think they have their own memory, containerized processes can have their own file system with a distinct /tmp, distinct process id namespace, or namespace of users that exist on the system. Every process can run as PID=1 if it wants, within its own PID namespace.)

These namespace primitives, from which containers are made, are present on modern Linux systems whether one chooses to employ them or not. The primary downsides to consider are efficiency of the system, and the complexity of managing it. If your system (CPU & OS kernel) implements virtual memory efficiently, then there isn’t much downside to using it. The same is probably true for most kernel name spaces, though file system and networking virtualization can have a performance hit if not configured with care.

Kernel namespaces are a core feature of Linux and can be taken advantage of without using technologies that are specifically "container-oriented". For example, consider systemd: it provides a comprehensive set of parameters for employing namespace features in processes that it launches. Parameters like PrivateTmp=yes or PrivateDevices= [1] will virtualize just one part of the system (/tmp or /dev and such, respectively). PrivateUsers= and PrivateNetwork= allow you to launch with a new user or network namespace. It's really that easy to employ namespaces: add a line to your application's unit file.

When you look at container technology as a set of system primitives, then it makes sense to consider employing them individually. They don't have to be used in an all-or-nothing way. You might give your daemon access to the regular network
with a private file system, or you might use the regular file system too while virtualizing just /tmp and /dev. You can isolate processes in whatever way makes sense, and share whatever resources make sense. If a process doesn't need access to the network, and doesn't need a shared /tmp with the rest of the system, then there's little downside to giving the process its own namespace. Indeed, I expect it will increasingly be considered a best practice for services to isolate themselves according to the principle of least privilege. This reduces the chance that components will interact with each other in unexpected and undesired ways, and may have some security benefits.

(If the question is about using Docker or some other specific technology as part of a development and/or deployment process, then that's a different topic. Specific technology suites have tradeoffs beyond those of kernel namespaces.)

[1] https://www.freedesktop.org/software/systemd/man/systemd.exe...