tl;dr: TLSDESC have solved most problems in formerly inefficient TLS access models, so I think we can drop TLS relaxation support from lld.
lld’s code to handle relocations is a mess; the code consists of a lot of cascading "if"s and needs a lot of prior knowledge to understand what it is doing. Honestly it is head-scratching and needs serious refactoring. I’m trying to simplify it to make it manageable again, and I’m now focusing on the TLS relaxations.
Thread-local variables in ELF is complicated. The ELF TLS specification  defines 4 different access models: General Dynamic, Local Dynamic, Initial Exec and Local Exec.
I’m not going into the details of the spec here, but the reason why we have so many different models for the same feature is because they were different in speed, and we have to use (formerly) slow models when we know less about their run-time memory layout at compile-time or link-time. So, there was a trade-off between generality and performance. For example, if you want to use thread-local variables in a dlopen(2)'able DSO, you need to choose the slowest model. If a linker knows at link-time that a more restricted access model is applicable (e.g. if it is linking a main executable, it knows for sure that it is not creating a DSO that will be used via dlopen), the linker is allowed to rewrite instructions to load thread-local variables to use a faster access model.
What makes the situation more complicated is the presence of a new method of accessing thread-local variables. After the ELF TLS spec was defined, TLSDESC  was proposed and implemented. With that method, General Dynamic and Local Dynamic models (that were pretty slow in the original spec) are as fast as much faster Initial Exec model. TLSDESC doesn’t have a trade-off of dlopen’ability and access speed. According to , it also reduces the size of generated DSOs. So it seems like TLSDESC is strictly a better way of accessing thread-local variables than the old way, and the thread-local variable’s performance problem (that the TLS ELF spec was trying to address by defining four different access models and relaxations in between) doesn’t seem a real issue anymore.
lld supports all TLS relaxations as defined by the ELF TLS spec. I accepted the patches to implement all these features without thinking hard enough about it, but on second thought, that was likely a wrong decision. Being a new linker, we don’t need to trace the history of the evolution of the ELF spec. Instead, we should have implemented whatever it makes sense now.
So, I’d like to propose we drop TLS relaxations from lld, including Initial Exec → Local Exec. Dropping IE→LE is strictly speaking a degradation, but I don’t think that is important. We don’t have optimizations for much more frequent variable access patterns such as locally-accessed variables that have GOT slots (which in theory we can skip GOT access because GOT slot values are known at link-time), so it is odd that we are only serious about TLS variables, which are usually much less important. Even if it would turn out that we want it after implementing more important relaxations, I’d like to drop it for now and reimplement it in a different way later.
This should greatly simplifies the code because it does not only reduce the complexity and amount of the existing code, but also reduces the amount of knowledge you need to have to read the code, without sacrificing performance of lld-generated files in practice.