There can be many reasons to why BBB-like barrier is not present in all the capillaries of the body. Let's talk about them one at a time.
Blood-brain barrier has its own side effects. Some major side effects are cerebral edema (accumulation of excess water in the extracellular space of the brain, which can result when hypoxia causes the blood–brain barrier to open) and (possibly) Epilepsy. See this wikipedia article:
Several clinical and experimental data have implicated the failure of blood–brain barrier function in triggering chronic or acute seizures. Some studies implicate the interactions between a common blood protein (albumin) and astrocytes. These findings suggest that acute seizures are a predictable consequence of disruption of the BBB by either artificial or inflammatory mechanisms.
Another problem is that BBB doesn't allow passage of drugs, diagnostic and therapeutic agents through it. Again, see this article:
Overcoming the difficulty of delivering therapeutic agents to specific regions of the brain presents a major challenge to treatment of most brain disorders. In its neuroprotective role, the blood–brain barrier functions to hinder the delivery of many potentially important diagnostic and therapeutic agents to the brain. Therapeutic molecules and antibodies that might otherwise be effective in diagnosis and therapy do not cross the BBB in adequate amounts.
Now, if you want to know why the body doesn't have BBB-like barrier (not exactly BBB), then there are three parts of the answer.
These kinds of barriers are highly specialized for a particular organ or organ system, which may not be useful for another organ/organ system. Also, creating specialized barriers for all the parts of the body will take a lot of energy, cells and even more time to develop completely. Possibly, in the evolutionary course, body preferred to have phagocytic cells circulating in the body instead of having specialized barriers throughout the body.
These barriers might not be a total solution for immunity or restriction of pathogens. See this part:
It is believed that latent HIV can cross the blood–brain barrier inside circulating monocytes in the bloodstream ("Trojan horse theory") within the first 14 days of infection. Once inside, these monocytes become activated and are transformed into macrophages. Activated macrophages release virions into the brain tissue proximate to brain microvessels. These viral particles likely attract the attention of sentinel brain microglia and perivascular macrophages initiating an inflammatory cascade that may cause a series of intracellular signaling in brain microvascular endothelial cells and damage the functional and structural integrity of the BBB. This inflammation is HIV encephalitis (HIVE).
Also, it is not necessary that those pathogens would infect only those tissues to which they reach via bloodstream. Pathogens like HIV cause infection in the blood cells. See this image from here:
Once a person is infected with HIV, the virus begins to attack and destroy the CD4 cells of the immune system. CD4 cells are a type of white blood cell that play a major role in protecting the body from infection. HIV uses the machinery of the CD4 cells to multiply (make copies of itself) and spread throughout the body. This process, which includes seven steps or stages, is called the HIV life cycle.
Similar barriers are already present in many parts of the body. For example- Blood-Ocular Barrier, Blood-Testis Barrier, Blood-Thymus Barrier, etc. They may also have some loopholes. For example, see this article-
Possible consequences of blood-thymus barrier failure are trophoblast-specific or tumor-specific antigens penetrate into the thymus, deletion or anergy of antigen-specific clones and acquired thymic tolerance induction.