It's been a while, since I studied this, but linear bounded automata are arguably a better model for the real computers we can actually build and the halting problem is computable for LBAs.
That said, in practice I'm not sure it is too useful (this is a slightly different question to the one originally asked, though). My understanding is the proof of decidability is essentially a pigeonhole principle argument based on LBA having a finite number of states: run the LBA for that many steps, if it hasn't halted, then it has looped. Even if a program is running on a system that only allows programs to use 1GB of memory, there's 2^(2^30*8) (approximately 10^(2.6e9)) states.
Essentially, the problem is not with computers, but with languages.
If your language lets you build a neverending loop/datastructure/etgc, then you cannot prove halting for all the programs that can be made by the language.
Since such languages exist, then by extension, it applies to computers.
That said, in practice I'm not sure it is too useful (this is a slightly different question to the one originally asked, though). My understanding is the proof of decidability is essentially a pigeonhole principle argument based on LBA having a finite number of states: run the LBA for that many steps, if it hasn't halted, then it has looped. Even if a program is running on a system that only allows programs to use 1GB of memory, there's 2^(2^30*8) (approximately 10^(2.6e9)) states.