This model makes very little sense in context of regular computer usage. It makes a lot more sense when you think of military style classifications, where it makes sense sometimes to write things to another level. For example, if you have a bunch of reports coming in to one analyzer, you want the singular report writers to just upload their stuff and never deal with it again. However, the guy that analyzes all the reports can operate at a higher level because of the increased classification of information, due to aggregation of information due to having multiple reports/sources of information.
Another thing you gotta keep in mind BLP is all about Confidentiality. The star property in particular is also called the 'confinement property' as it supposed to prevent information traversing multiple levels. You want each subject to be able to read or write from particular levels and that's it, no other abilities limit the possibility of the information traversing outside of it's designated level. This property makes sure you cannot grab information that's not for you (no read up), and cannot give away the information to lower levels (no write down).
The Strong Star Property makes the limitations even more stringent, as it changes 'no read up, no write down' to 'no read up, write only to same'. This way you cannot 'write up' and upclassify documents, which is desireable, unless you actually need it.
All of these are just more precise formulation of the general Principle of Least Privilege, with respect to confidentiality.