And I've only recently found out that SSDs apparently need to have their partition "start offset" aligned to something exactly divisible by 4 (in Msinfo32 - the winDoze "inspecting"/reporting app) in order to be "properly aligned".
In fact, it is a little more complicated, because the various SSD drive models don't use the same identical internal format. The relevant seems to be the minimum segment size that the specific drive uses to write on the "disk" space.
The old legacy rotational drives are able to write one sector only (512 bytes). The various memory-based media (SSD drives, flash usb sticks, memory cards ... ) use much larger segments to write at once, although the sector size is 4KiB ( i.e. 8 "old"sectors). This segment size varies for the models and manufacturers, up to 64KiB, 128KiB, even 256KiB as fas as I know. This could change in the future, as the SSD technology is constantly evolving. So, the operating systems chose to use 1MiB to align their partitions, because this is a multiple of every segment size used. Using 64KiB alignment would be a problem for drives with larger segment organisation.
On the other hand, 1 MiB is much lower than the old cylinder size, that was almost 8 MiB (16065 sectors).
Of course, it would be possible to work well with an SSD drive aligned exactly to the segment size of that specific model (64KiB or 32KiB or so... ). However, this would complicate much more the format process and the hardware versatility.
You are right that the CHS concept is really irrelevant for the operating systems now, and this since early or mid 1990s. It was however more relevant for the BIOS.
The main problem with the SSD drives, in my mind, is that their optimal use needs an entirely new system concept, from the hardware and software points of view. Actually, the operating systems or maintenance tools don't really support the 4KiB sector format, so the drive firmware emulates a 512-byte scheme. UEFI BIOS and GPT were designed to be more compatible with newer hardware and software concepts, but legacy solutions are the majority in the small personal computer world.
Regarding the issue of the original post, it could be a driver problem too: windows xp used the IDE drivers during installation. To use a fully SATA configured hard drive (i.e. in AHCI mode), special drivers were needed to provide in floppy disk (it was similar for motherboard-based RAID array configuration). In this case, to easily migrate the system, it is better to use the hard drive in IDE emulation, loosing the AHCI benefits (higher data transfer rate, HD replacement without need to power down the system).
*** It is highly recommended to backup any important files before doing resize/move operations. ***