Prokaryotic organisms don’t have membrane-bound organelles because, from certain point of view, they ARE membrane-bound organelles! This is oversimplificated and overgeneralised statement, of course, but let us take a closer look. ;-)

For understanding of the difference between prokaryotes and eukaryotes, it may be benefical to look a few bilion years to the past of our planet. Until some 2 bilion years ago, the world was dominated by relatively “simple” cellular organisms similar to nowadays Bacteria (incl. Cyanobacteria) and extremophilic Archea (i.e. prokaryotes). Their cytoplasmatic membrane enveloped cytoplasm (the solution of water, minerals and organic compounds) in which only basic components absolutely necessary for life were freely floating. These involved, for example, ring-shaped molecule of double-stranded DNA (called nucleoid) and ribosomes (in which genes written in the DNA are translated into the proteins which, subsequently, serve as enzymes, building blocks etc.). That’s how prokaryotes look like.

The revolutional steps in the evolution of life on Earth were so called endosymbiotic events. This means that these “simple” prokaryotic cells merged together (I believe that the leading opinion among scientists nowadays is that during the first successful endosymbiosis, the Archeal organism swallowed Bacteria with aerobic metabolism, though I am not active in the field of endosymbiosis research) and started to live as a single organism. When bacteria was swallowed, somehow it was not digested but rather survived and reproduced (i.e. simply divided) within the host cell. When time comes the host also divided and each of its daughter cells now contained these bacteria symbionts within its cytoplasm. Bacterial symbionts now lived in a completely new environment than before (inside of the cytoplasm vs. open water), more “safe” let’s say, so sudenly it had no use for many things it evolved to survive and reproduce during its previous free-living era (e.g. some genes, motility structures etc.). So it started to loss some structures, genes and functions and, eventually, became a mitochondria. Such simplification is common in endoparasites, for example, because they also lost features that have no use in a new environment within the host body. In any case, old cytoplasmatic membranes of bacteria symbiont are homologous to (at least one of the ) membranes of mitochondria. In a similar way chloroplasts originated (only photosynthetic cyanobacteria was swallowed) etc.

Increasing complexity of the cell body along with increasing concantration of free elemental oxygen in the environment due to activity of cyanobacteria, allowed for much more efficient oxygen-based metabolism (or more precisely metabolism in which oxygen, which is the most efficient for the purpose, serve as an acceptor of electrons in the metabolic pathways responsible for producing energy) and caused rapid cellular evolution which, in series of steps, resulted in a modern days eukaryotic cells. Some membrane organels (e,g, nucleus), however, are not result of endosymbiosis but rather of folding of the host’s own cytoplasmatic membrane. So in eukaryotic cell you have clearly separated compartments by membranes in which you can perform different biochemical reaction separately (and you can simultaneously run even ractions which would inhibit one another if held in the same space) which significantly widens your biochemical options and allows for more efficient energetic economy. And since in nature everything is about flow and utilization of energy, these organisms (at least) survived or even outcompeted (from certain point of view) their prokaryotic ancestors. By the way, we know that mitochondria and chloroplasts are the results of endosymbiosis (where symbiont was bacteria and cyanobacteria, respectively) because they remained remnants of their former nucleoid. This DNA can then be used in phylogenetic analyses where chloroplasts, for example, appear within the phylogenetic tree of the cyanobacteria. So from evolutionary point of view, chloroplasts are simply a cyanobacteria adapted to symbiotically live within other cells and mitochondria are aerobic bacteria adapted to symbiotical relationship.

Introduction
Prokaryotic cells are single-celled organisms that lack a nucleus and membrane-bound organelles. They are simpler in structure than eukaryotic cells, which have a nucleus and various organelles. One of the main differences between prokaryotic and eukaryotic cells is the absence of membrane-bound organelles in prokaryotic cells. In this response, we shall look at the reasons why prokaryotic cells lack membrane-bound organelles.

The Absence of Membrane-bound Organelles in Prokaryotic Cells
Prokaryotic cells do not contain membrane-bound organelles such as mitochondria, chloroplasts, endoplasmic reticulum, and Golgi apparatus, among others. There are several reasons for this:

Simplicity of Prokaryotic Cells
Prokaryotic cells are simpler in structure than eukaryotic cells. They lack a nucleus and other membrane-bound organelles, making them more streamlined for their basic functions. They have a simple structure with a cell wall, cell membrane, cytoplasm, and ribosomes. This simplicity allows them to carry out their essential functions, including reproduction, metabolism, and gene expression.

Size Limitations
Prokaryotic cells are typically smaller than eukaryotic cells. The small size of prokaryotic cells makes it difficult to accommodate membrane-bound organelles. The size of the cell membrane in prokaryotic cells is limited, and adding more membranes would reduce the space available for essential functions.

Efficient Nutrient Uptake
Prokaryotic cells have a high surface-to-volume ratio, which means that they can efficiently take up nutrients from their environment. The absence of membrane-bound organelles allows them to maximize the surface area available for nutrient uptake. Nutrients diffuse across the cell membrane and into the cytoplasm, where they are used for various cellular processes.

Conclusion
Prokaryotic cells lack membrane-bound organelles due to their simplicity, size limitations, and efficient nutrient uptake. These cells have evolved to perform their essential functions without the need for specialized organelles. The absence of membrane-bound organelles does not limit their ability to carry out essential life processes.