I have seen answers like Time efficiency and compatibility. those are The Reasons, but I do not think it is explained why these are sometime necessary in times like ours. from all answers and experience of chatting with other engineers I have seen it pictured as some sort of quirky old time way of doing things that should just die because new way to do things are better.
Yes, in very rare case you may want to do it the "old way" for performance sake like if you have the classic million times loop. but I say that is the wrong perspective of putting things.
While it is true that you should NOT care at all and use whatever C# language throws at you as the new right-way™ to do things (enforced by some fancy AI code analysis slaping you whenever you do not meet their code style), you should understand deeply that low level strategies aren't there randomly and even more, it is in many cases the only way to solve things when you have no help from a fancy framework. your OS, drivers, and even more the .NET itself(especially the garbage collector) are built using bitfields and transactional instructions. your CPU instruction set itself is a very complex bitfield, so JIT compilers will encode their output using complex bit processing and few hardcoded bitfields so that the CPU can execute them correctly.
When we talk about performance things have a much larger impact than people imagine, today more then ever especially when you start considering multicores.
when multicore systems started to become more common all CPU manufacturer started to mitigate the issues of SMP with the addition of dedicated transactional memory access instructions while these were made specifically to mitigate the near impossible task to make multiple CPUs to cooperate at kernel level without a huge drop in perfomrance it actually provides additional benefits like an OS independent way to boost low level part of most programs. basically your program can use CPU assisted instructions to perform memory changes to integers sized memory locations, that is, a read-modify-write where the "modify" part can be anything you want but most common patterns are a combination of set/clear/increment.
usually the CPU simply monitors if there is any other CPU accessing the same address location and if a contention happens it usually stops the operation to be committed to memory and signals the event to the application within the same instruction. this seems trivial task but superscaler CPU (each core has multiple ALUs allowing instruction parallelism), multi-level cache (some private to each core, some shared on a cluster of CPU) and Non-Uniform-Memory-Access systems (check threadripper CPU) makes things difficult to keep coherent, luckily the smartest people in the world work to boost performance and keep all these things happening correctly. todays CPU have a large amount of transistor dedicated to this task so that caches and our read-modify-write transactions work correctly.
C# allows you to use the most common transactional memory access patterns using Interlocked class (it is only a limited set for example a very useful clear mask and increment is missing, but you can always use CompareExchange instead which gets very close to the same performance).
To achieve the same result using a array of booleans you must use some sort of lock and in case of contention the lock is several orders of magnitude less permorming compared to the atomic instructions.
here are some examples of highly appreciated HW assisted transaction access using bitfields which would require a completely different strategy without them of course these are not part of C# scope:
assume a DMA peripheral that has a set of DMA channels, let say 20 (but any number up to the maximum number of bits of the interlock integer will do). When any peripheral's interrupt that might execute at any time, including your beloved OS and from any core of your 32-core latest gen wants a DMA channel you want to allocate a DMA channel (assign it to the peripheral) and use it. a bitfield will cover all those requirements and will use just a dozen of instructions to perform the allocation, which are inlineable within the requesting code. basically you cannot go faster then this and your code is just few functions, basically we delegate the hard part to the HW to solve the problem, constraints: bitfield only
assume a peripheral that to perform its duty requires some working space in normal RAM memory. for example assume a high speed I/O peripheral that uses scatter-gather DMA, in short it uses a fixed-size block of RAM populated with the description (btw the descriptor is itself made of bitfields) of the next transfer and chained one to each other creating a FIFO queue of transfers in RAM. the application prepares the descriptors first and then it chains with the tail of the current transfers without ever pausing the controller (not even disabling the interrupts). the allocation/deallocation of such descriptors can be made using bitfield and transactional instructions so when it is shared between diffent CPUs and between the driver interrupt and the kernel all will still work without conflicts. one usage case would be the kernel allocates atomically descriptors without stopping or disabling interrupts and without additional locks (the bitfield itself is the lock), the interrupt deallocates when the transfer completes.
most old strategies were to preallocate the resources and force the application to free after usage.
If you ever need to use multitask on steriods C# allows you to use either Threads + Interlocked, but lately C# introduced lightweight Tasks, guess how it is made? transactional memory access using Interlocked class. So you likely do not need to reinvent the wheel any of the low level part is already covered and well engineered.
so the idea is, let smart people (not me, I am a common developer like you) solve the hard part for you and just enjoy general purpose computing platform like C#. if you still see some remnants of these parts is because someone may still need to interface with worlds outside .NET and access some driver or system calls for example requiring you to know how to build a descriptor and put each bit in the right place. do not being mad at those people, they made our jobs possible.
In short : Interlocked + bitfields. incredibly powerful, don't use it