The big drawback to various nonprobability methods is in the area of inference to the population of interest. Snowball (respondent-driven) sampling seems the only method which may not require additional aid. The following article notes that the sample size needs to be much larger than that for simple random sampling, but it seems that this method better avoids bias than other nonprobability methods. See Salganik, M.J.(2006), "Variance Estimation, Design Effects, and Sample Size Calculations for Respondent-Driven Sampling," Journal of Urban Health, 83, pp. 98-112. But this is not my area, and I don't know how well accepted this may be.
My area is model-based (i.e., prediction/regression) methodology.
In general, for a nonprobability sample to be useful to infer to a population, you need a good predictor as shown in
Valliant, R, Dorfman, A.H., and Royall, R.M.(2000), Finite Population Sampling and Inference: A Prediction Approach, Wiley Series in Probability and Statistics,
Chambers, R, and Clark, R(2012), An Introduction to Model-Based Survey Sampling with Applications, Oxford Statistical Science Series,
Or
Knaub(2022), "Application of Efficient Sampling with Prediction for Skewed Data," JSM 2022:
More research is being done in this area now. Still, in perhaps most ad hoc situations, inference from nonprobability sampling is not good. However, in repeated official surveys with an occasional census, using prediction (i.e., regression), where there is strong knowledge of the populations, this can be quite accurate, as work I began in 1990 at a statistical agency has repeatedly shown.
Of interest may be the following:
Kyu-Seong Kim(2022), Methodology of Non-probability Sampling in Survey Research," American Journal of Biomedical Science and Research, 15(6), Mini Review,
1. Convenient - Sample selected depending on what is convenient for the researcher
2. Quota system - Identifying a given quota then from the population you pick any respondent without caring about the fair representation of the target population
3. Judgmental - Where a research subjectively decide who to be part of the respondents