As you say, mostly shaving one's beard is considered forbidden:
The four Sunni schools of Islamic law (madhhabs) also quite clearly mention the impermissibility of shaving the beard
However, there are exceptions (where it's only recommended):
Trimming or shortening one’s beard is not illegal according to all [four]
Imams. Growing the beard is described as obligatory, or recommended.
Likewise, the scholars disagreed over whether a Muslim man can shave his
beard off; some considered this haram, while others did not.
If you're incapable of growing a (full) beard, then you can't be held responsible for it:
(' Abd al-Wahhab Khallaf:) Three conditions must exist in any act that it is legally valid to make an individual responsible for. ... The third condition is that the act the subject is responsible for be possible and within the capacity of the subject to do or to refrain from.
The Reliance of the Traveller, by Ahmad ibn Naqib al-Misri, translated by Nuh Ha Mim Keller
Having a half-beard is probably going to look abnormal and draw unfavorable attention, in which case there's the possibility of dispensation. The closest fatwa I found to the stated question is:
In any case, the questioner stated that his beard mostly grows on the cheeks (with much less growing on the bottom of the face) and looks strange and unnatural. If this makes his face look abnormal and it harms him, then he may trim it to the extent that wards off the harm.
Another IslamWeb fatwa permits a hair transplantation. IslamWeb's fatwa is likely to be among the stricter rulings in Sunni Islam. The ruling seems comparable in Shia Islam:
A Muslim is allowed to shave his beard, if he is compelled to do so or if he is forced to shave it for medical reasons, etc. It also allowed if he fears harm to his life by not shaving or if growing the beard would put him in difficulty (for example, if it becomes a cause of ridicule and humiliation that is not normally tolerable by a Muslim).
Ayatollah Sistani, sistani.org