Why GTA genes can't be maintained by 'selfish' transmission

Below is the line of reasoning showing that the genes responsible for producing GTA particles cannot maintain themselves or spread into new populations by GTA-mediated transfer of themselves into new cells.  I initially worked this out with a rigorous set of mathematical equations, but then realized that the problem was so glaringly obvious that math isn't needed.

The main GTA gene cluster is too big to fit inside a single GTA particle, so GTA particles can't transmit DNA that converts a GTA- cell into a GTA+ cell.  Some genes outside the main cluster are also required for GTA production.

But GTA particles can (and do) contain one or more individual GTA genes.  If a fragment containing a particular GTA gene is injected into a formerly-GTA+ cell that is now GTA- because it has a mutated version of this gene, the resulting recombination can restore the cell's original GTA+ genotype.

But these transfer events would not allow GTA+ cells to invade a GTA- population, or to maintain themselves in the face of loss of GTA function by mutation.  That's true for all known GTA systems, even in the simplest (imaginary) case where production of GTA particles requires only a single gene that could easily fit into a GTA particle, as illustrated below.  

Why?  Three factors together require that production of GTA particles reduces the total number of GTA+ cells in the population:

Problem 1:  GTA particles can only be released to the environment if the GTA+ producer cell lyses.  So each production event removes one GTA+ cell from the population.

Problem 2:  The GTA genes in the producer cell are not over-replicated as a phage genome would be, so each production event can produce at most one G+ particle (containing the GTA gene or cluster).  

If all steps occurred with 100% efficiency, problems 1 and 2 would allow, at best, replacement of the lost GTA+ cell with a new one created by GTA-mediated recombination.  But this would not maintain the numbers of GTA+ cells in the face of occasional loss of GTA genes by mutation or deletion.  Nor would it allow GTA+ cells to invade a GTA- population.

Problem 3:   Production of GTA particle production, transmission of their DNA to recipient cells, and recombination with the recipient genome are all likely to be at least moderately inefficient.  Here's a partial list of expected inefficiencies:

1. Burst size:  Actual burst sizes are unknown, but packaging all the DNA in a R.capsulatus. genome would need 841 particles, which is much larger than typical burst sizes for DNA phages.  Capsid proteins may be limiting, since they would be produced from single-copy GTA genes rather than replicated phage genomes.
2. Dispersion:  The GTA particles will disperse in the environment, and many will probably not find cells to attach to.
3. Stability:  Lab preps of GTA particles are unstable in non-optimal storage conditions, so many particles will likely fall apart.
4. Recombination efficiency:  Only one DNA strand enters the cytoplasm, and some DNA degradation is likely.  The highest observed transduction frequency is only ~4^-4, (theor. max: 1.2^-3) so recombination efficiency is probably only ~0.3.  Recombining in a novel gene will be less efficient than simple strand replacement
5. Self-conversion:  Some G+ particles may attach to cells that are already GTA+.