Fun game! Though I dispute that people are "very close" to achieving a perfect pattern.

To get a "perfect" pattern you'd need to find three 7 letter words that can stack on rows adjacent to each other to form a 3 letter word in each column. Such arrangements do exist, for example:

    o p e r a t e
    a r r o w e d
    r e s e n d s

but they are very rare - I estimate something on the order of 0.002% of combinations of three 7-letter words have any valid arrangements. Assuming that you're using standard ETAOIN letter frequencies, the typical bag of 21 letters will usually have just a handful of combinations of three 7-letter words so a given puzzle has a << 0.1% chance of having a perfect solution.

But there are 12,000x more ways to rearrange 21 tiles within an 8x3 grid, and the word choices are more forgiving as well (if you draw 7 letters from the etaoin frequency distribution, those 7 letters in order are much more likely to form a 3 letter word followed by a 4 letter word than they are to form a 7 letter word). Pretty much every puzzle should have at least some solutions fitting within an 8x3.

Additional note: 3 blank spaces is the best non-perfect arrangement, since the grid is only 10 tiles wide. One blank space could only be achieved by a single 23-letter-long word, and two blank spaces could only be achieved by a 10 letter word next to an 11 letter word, and an 11 letter word would not fit inside the 10x10 grid.